Mock Test Attempt

1. The average of 9 observations was 9, that of the first 5 being 10 and that of the last 5 being 8. What was the fifth observation ?

A. 8

B. 7

C. 9

D. 10

Given: • Average of 9 numbers = 9 - Total = 9 × 9 = 81 • Average of first 5 numbers = 10 - Total = 10 × 5 = 50 • Average of last 5 numbers = 8 - Total = 8 × 5 = 40 The 5th number is counted in both the first and last 5 numbers. So: Add both totals:50 + 40 = 90 But the real total is only 81, so the 5th number was counted twice. To fix that, subtract the extra 5th number once: 90 - x = 81 → x = 9 Answer: 5th observation is 9.

2. Consider the five numbers given here : (i) 736 (ii) 269 (iii) 958 (iv) 219 (v) 793 Arrange the digits of each number in descending order. What would be the difference between the highest number and the lowest one ?

A. 222

B. 716

C. 618

D. 12

Given Numbers: 736, 269, 958, 219, 793 Rearrange digits in descending order: • 736 - 763 • 269 - 962 • 958 - 985 • 219 - 921 • 793 - 973 Find highest and lowest: • Highest = 985 • Lowest = 763 Find the difference: 985 − 763 = 222 Ans: 222

3. The longest diagonal that can be found in a regular cube of side 1 cm is :

A. 2 cm

B. sqrt 2 cm

C. 3 cm

D. sqrt 3 cm

Formula: Longest diagonal of a cube = side × √3 Given: Side = 1 cm Calculation: 1 × √3 = √3 cm Ans: √3 cm

4. Three numbers A, B and C are such that the HCF of A and B is same as the HCF of B and C. If the LCM of A and B is three times the LCM of B and C, then the ratio C : A is :

A. 1 : 9

B. 3 : 1

C. 9 : 1

D. 1 : 3

Given: • HCF(A, B) = HCF(B, C) • LCM(A, B) = 3 × LCM(B, C) • We need to find the ratio C : A Let: • A = d × a • B = d × b • C = d × c (Where d is the common HCF, and a, b, c are co-prime) LCM(A, B) = d × a × b LCM(B, C) = d × b × c Given: LCM(A, B) = 3 × LCM(B, C) d × a × b = 3 × d × b × c Cancel d × b from both sides: a = 3c So: A = d × a = d × 3c C = d × c Therefore: C / A = (d × c) / (d × 3c) = 1 / 3 Ans: C : A = 1 : 3

5. At a class test for 50 students, the average score was found to be 45.5 out of 100. Upon checking, it was found that an incorrect data-entry had occurred where 85 was incorrectly entered as 58. What should be the correct class average ?

A. 54.50

B. 46.04

C. 46.40

D. 55.40

Total score using wrong average • 45.5 × 50 = 2275 Correct the wrong score • Wrong entry: 58 • Correct score: 85 • Difference = 85 − 58 = 27 Correct total score • 2275 + 27 = 2302 Correct average • 2302 ÷ 50 = 46.04 Correct average is: 46.04

6. If cosθ= 5/13 , then the value of sinθ is :

A. 5/12

B. 12/5

C. 12/13

D. 13/12

Given: Cosθ = 5/13 Use identity: sin2θ + cos2θ = 1 Plug in value: sin2θ+(5/13)2=1 = sin2θ+25/169 = 1 Solve for sin2θ: sin2θ=1−25/169=144/169 Take square root: Sinθ = 12/13 Ans: Sinθ=12/13

7. The remainder when −46 is divided by 3 is :

A. −2

B. −1

C. 1

D. 2

Find a number that multiplies with 3 close to – 46 • 3 × (–16) = –48 Now: – 46 – (– 48) = –46 + 48 = 2 Ans: The remainder is 2

8. If Pn represents the product of the natural numbers from 1 to n, then P1+P2+P3+P4 is :

A. 23

B. 33

C. 37

D. 31

To find P1+P2+P3+P4, we first need to calculate the factorials for each value of nn: <ul> <li>P1=1!=1</li> <li>P2=2!=2×1=2 </li> <li>P3=3!=3×2×1=6 </li> <li>P4=4!=4×3×2×1=24</li> </ul> Now, we sum them up: P1+P2+P3+P4=1+2+6+24 Calculating the sum: 1+2=3 3+6=9 9+24=33 Thus, the value of P1+P2+P3+P4 is: (B) 33.

9. A cone has a base radius of 4 cm and height of 9 cm. The volume of the cone is :

A. 36π cm3

B. 48π cm3

C. 13π cm3

D. 24π cm3

Volume of a Cone Formula: V=1/3πr2h Given: • Radius (r) = 4 cm • Height (h) = 9 cm Step-by-step: • Square the radius: r2=42=16 • Multiply: 16×9=144 • Multiply by 1/3 : 1/3×144=48 Add π: V=48π cm3 Ans: Volume = 48π cm³

10. If sinθ=cosθ then the value of 1+tanθ is :

A. 1

B. 2

C. 0

D. sqrt 2

Given: Sinθ = Cosθ Divide both sides by Cosθ Sinθ / Cosθ = Cosθ/cosθ tanθ=1 Add 1 to tanθ 1+tanθ = 1+1 = 2 Ans: 2

11. The least natural number which when divided by 2 gives remainder 1, when divided by 3 gives remainder 2 and when divided by 4 gives remainder 3, is :

A. 23

B. 17

C. 31

D. 11

We are given: • N = 1(mod 2) • N = 2(mod 3) • N = 3(mod 4) Notice a pattern We can rewrite each condition like this: • N+1 is divisible by 2 • N+1 is divisible by 3 • N+1 is divisible by 4 So: N+1 is a common multiple of 2,3,4 Find the least common multiple (LCM) LCM(2,3,4)=12 So: N+1=12 ⇒ N=11 But 11 doesn't work for all conditions. Try: N+1=24 ⇒ N=23 Check N=23 • 23mod 2=1 • 23mod 3=2 • 23mod 4=3 Ans: 23 is the smallest natural number that satisfies all 3 conditions.

12. 72 toffees were distributed to some boys in a group. Each boy in the group got twice as many of the toffees as the number of boys. The number of boys in the group is :

A. 6

B. 7

C. 8

D. 9

Given: • Each boy gets 2×(number of boys) toffees. • Total toffees = 72 Let number of boys = x • Each boy gets 2x toffees • Total toffees = x × 2x = 2x² So: 2x²=72 Solve: x² = 36 (Divide both sides by 2) x = 6 (Take square root) Ans: Number of boys = 6

13. The product of the roots of the quadratic equation 2x2−5x+6=0 is :

A. 2

B. 3

C. 5

D. 6

Given equation: 2x^2−5x+6=0 Coefficients: • a=2 • b=−5 • c=6 Formula for product of roots: Product of roots = c/a Substitute values: 6/2 = 3 Final Answer: Product of the roots = 3

14. Grandmother was cooking at a picnic, attended by her son and daughter-in-law, with their four sons and their wives and one son and two daughters to each of the sons. How many ladies were there at the picnic ?

A. 8

B. 12

C. 14

D. 10

Who were at the picnic ? • 1 Grandmother • 1 Daughter-in-law • 4 Sons, each with: 1 Wife - 4 Ladies 2 Daughters each - 4 × 2 = 8 Girls Total Ladies: • Grandmother = 1 • Daughter-in-law = 1 • Wives = 4 • Daughters = 8 Ans: Total Ladies = 1 + 1 + 4 + 8 = 14

15. squrt 225/729- squrt 25/144-squrt 16/81= ?

A. − 7 / 12

B. − 20 / 27

C. − 5 / 9

D. − 11 / 36

To simplify the expression sqrt 225 / 729 - sqrt 25 / 144 - sqrt 16 / 81 Each square root: <ul> <li style="list-style-type: none;"> <ul> <li>sqrt 225/729   225729=15/27 = 5/9</li> <li>sqrt 25/144=5/12</li> <li>sqrt 16/81=4/9</li> </ul> </li> </ul> Substitute these values back: 5/9−5/12−4/9 Find a common denominator (36): <ul> <li style="list-style-type: none;"> <ul> <li>Convert 5/9=20/36</li> <li>Convert 5/12=15/36</li> <li>Convert 4/9=16/36</li> </ul> </li> </ul> Perform the subtraction: 20/36−15/36−16/36=20−15−16/36 = −11/36

16. Identify the incorrect term in the series. {5, 8, 13, 20, 31, 40, 53}

A. 13

B. 31

C. 20

D. 40

Given Sequence: 5, 8, 13, 20, 31, 40, 53 Find the differences between terms • 8 − 5 = 3 • 13 − 8 = 5 • 20 − 13 = 7 • 31 − 20 = 11 • 40 − 31 = 9 - Wrong • 53 − 40 = 13 Look at the pattern The differences are: 3, 5, 7, 11, 9, 13 This is not a smooth increasing pattern. After 7, we expect 9, but instead we got 11, and then the next is 9. Conclusion: • The number 40 breaks the expected pattern. • So, 40 is the incorrect number in the sequence. Ans: Incorrect term is 40

17. What would replace # in the sets ? {5, 120, 3}, {9, 630, 5}, {9, 810, #}

A. 8

B. 7

C. 6

D. 4

Set: {5, 120, 3} • Take the middle number: 120 • Divide it by the first number: 120 ÷ 5 = 24 • Now divide that result by the last number: 24 ÷ 3 = 8 So the pattern is: Middle ÷ First ÷ Last = 8 Set: {9, 630, 5} • 630 ÷ 9 = 70 • 70 ÷ 5 = 14 Pattern again: Middle ÷ First ÷ Last = 14 Set: {9, 810, ?} find ? • 810 ÷ 9 = 90 • We want 90 ÷ ? = 15 So: ? = 90 ÷ 15 = 6 Ans: The missing number is 6

18. A person purchases x number of items at the rate of ` x per item. The shop-keeper gives him a total discount of ` x after which he pays ` 156. The cost per item after the discount is :

A. 13

B. 12

C. 16

D. 14

Problem: A person buys x items at ₹x each. He gets a discount of ₹x in total. He paid ₹156 after the discount. Solution: Total Cost without Discount If each item costs ₹x and he buys x items, Total cost = x × x = x² Discount Discount = ₹x Amount Paid So, total paid = x² - x We’re told: x² - x = 156 Solve the Equation: x² - x = 156 x² - x - 156 = 0 Now factor it: (x - 13)(x + 12) = 0 So, x = 13 or -12 We ignore -12 because x must be positive. Final Calculation: • x = 13 • Original cost per item = ₹13 • Discount = ₹13 total = ₹1 per item • New price per item = 13 - 1 = ₹12 Ans: Cost per item after discount = ₹12

19. The population of a town increases at the rate of 10% every year. If the present population of the town is 10,000, then after 3 years the population of the town would be :

A. 13,310

B. 15,310

C. 13,510

D. 13,000

To find the population of a town after 3 years with a 10% annual increase: <ol> <li>Current Population: 10,000</li> <li>Growth Rate: 10% (or 0.10)</li> </ol> Formula: Future Population = Current Population × (1 + Growth Rate) ^ Number of Years Calculation: Future Population  = 10,000 × (1 + 0.10)^3                               = 10,000 × (1.10)^3                               = 10,000 × 1.331 Future Population ≈ 13,310 So, after 3 years, the population will be 13,310.

20. The value of 0.09 + 1.69 is :

A. 1.78

B. 1.6

C. 1.33

D. 1.5

To find the value of 0.09+1.69 0.09 + 1.69 0.09+1.69=1.78 Therefore, the correct answer is (A) 1.78.

21. The addition of two binary numbers 11 and 10, when represented in binary system is :

A. 101

B. 110

C. 010

D. 111

Let's addition of the binary numbers 11 and 10 . First, let's break down the binary numbers: - The binary number 11 is equal to 3 in decimal (base 10). - The binary number 10 is equal to 2 in decimal (base 10). Now, let's add them in decimal to check our work:     3 (from 11) + 2 (from 10) = 5 in decimal. Next, we need to convert the decimal result (5) back into binary. To convert 5 to binary: - 5 divided by 2 is 2, remainder 1. - 2 divided by 2 is 1, remainder 0. - 1 divided by 2 is 0, remainder 1. Now, we read the remainders from bottom to top: 101. So, in binary, 3 (11) + 2 (10) equals 101. Thus, the correct answer is: A. 101

22. The three angles of a triangle are in the ratio of 1 : 3 : 5. The largest angle of the triangle is :

A. 70 Deg

B. 90 Deg

C. 120 Deg

D. 100 Deg

Solution: <ol> <li> Angles Ratio: Let the angles be 1x,3x,5x. </li> <li> Sum of Angles: In a triangle, the sum is 180∘: 1x+3x+5x=180∘ ⟹ 9x=180∘</li> <li> Solve for x: x=20∘</li> <li> Calculate Angles: <ul> <li>First angle: 1x=20∘ </li> <li>Second angle: 3x=60∘ </li> <li>Largest angle: 5x=100∘ </li> </ul> </li> </ol> So, the largest angle is 100°. Final Answer: (D) 100°.

23. The sum of the roots of the quadratic equation 2x2−5x+3=0 is :

A. 2

B. 3/2

C. 5/2

D. 5

The sum of the roots of the quadratic equation 2x2−5x+3=0  is calculated using the formula: Sum of roots=−b/a where a=2, b=−5. Substituting in those values: Sum of roots=−5/2

24. A person moves from P to Q in a semi-circular path and then comes back to P by the shortest route, which is 4 km. The total path covered by the person in the entire journey is :

A. (4π+2) km

B. (2π+4) km

C. (π+2) km

D. (2π+2) km

To solve this, we need to consider two parts of the person's journey: <ol> <li>The person moves from P to Q along a semi-circular path.</li> <li>The person returns to P from Q by the shortest route, which is the diameter of the circle and is given as 4 km.</li> </ol> <h3>Understanding the circular path</h3> <ul> <li>The shortest route between P and Q is the diameter, which means the diameter of the circle is 4 km.</li> <li>The radius rr of the circle can be found using the formula r=diameter2r = \frac{\text{diameter}}{2}, so r=42=2r = \frac{4}{2} = 2 km.</li> </ul> <h3>Semi-circular path</h3> <ul> <li>The distance traveled from P to Q along the semi-circular path is half the circumference of the circle.</li> <li>The formula for the circumference of a circle is 2πr2\pi r.</li> <li>For the semi-circular path, the distance is half the circumference:</li> <li>Distance from P to Q=πr=π×2=2π km</li> </ul> <h3>Total distance covered</h3> <ul> <li>The person first covers the semi-circular path from P to Q (which is 2π2\pi km).</li> <li>Then they return along the diameter, which is 4 km.</li> <li>The total distance traveled is = 2π+4 km</li> </ul>

25. A tank can be filled by 6 pipes in 80 minutes. How long will it take to fill the tank by 8 pipes ?

A. 45 min

B. 60 min

C. 48 min

D. 70 min

To find out how long it will take to fill the tank with 8 pipes : Work Done by 6 Pipes: 6 pipes can fill the tank in 80 minutes.  Rate of 1 Pipe: The rate for one pipe is: Rate of 1 pipe=180÷6=1480 tank per minute Rate of 8 Pipes: The rate of 8 pipes is: Rate of 8 pipes=8×1480=8480=160 tank per minute Time for 8 Pipes to Fill the Tank: Time=1 tank160 tank per minute=60 minutes So, it will take 60 minutes for 8 pipes to fill the tank.

26. (1% of 1)+(2% of 2)+(3% of 3)=?

A. 0.06

B. 0.6

C. 0.41

D. 0.14

To calculate (1% of 1)+(2% of 2)+(3% of 3): Calculate each percentage: <ul> <li style="list-style-type: none;"> <ul> <li>1% of 1=1100×1 = 0.01</li> </ul> </li> </ul> <ul> <li style="list-style-type: none;"> <ul> <li>2% of 2=2100×2=0.04</li> </ul> </li> </ul> <ul> <li style="list-style-type: none;"> <ul> <li>3% of 3=3100×3=0.09 </li> </ul> </li> </ul> Add them : 0.01+0.04+0.09=0.14

27. The product of the mean and the median of the data set 1, 0, −5, 3, 0, −2, 4, 6, −4, 1, 2 is :

A. 5/12

B. 7/13

C. 6/11

D. 9/14

<h3>Calculate the Mean</h3> Mean formula: Mean=Sum of all values/Number of values Sum of the values: 1+0+(−5)+3+0+(−2)+4+6+(−4)+1+2=6 Number of values: 11 Mean: Mean=6/11 <h3>Calculate the Median</h3> To find the median, we first need to sort the data set: Sorted data set: −5,−4,−2,0,0,1,1,2,3,4,6 Since there are 11 values (an odd number), the median is the middle value, which is the 6th value in the sorted list. Median: Median=1 <h3>Calculate the Product of the Mean and Median</h3> Now, we find the product of the mean and the median: Product=Mean×Median=6/11×1=6/11

28. A person borrows a sum of ` 1,00,000 at a simple interest of 6% per annum for 2 years and invests the amount at a compound interest of 6% per annum for 2 years. After returning the borrowed amount with interest, the person earns a profit of :

A. 360

B. 120

C. 480

D. 240

<h3>Calculating Simple Interest on Borrowed Amount</h3> <ul> <li>Principal Amount (P): 1,00,000</li> <li>Rate of Interest (R): 6% per annum or 0.06</li> <li>Time (T): 2 Years</li> </ul> Simple Interest (SI) is calculated using the formula: SI=P×R×T SI=1,00,000×0.06×2=12,000\text{SI} = 1,00,000 \times 0.06 \times 2 = 12,000 <h3>Total Amount to be Returned</h3> <ul> <li>The total amount to be returned after 2 years (Principal + Simple Interest):</li> </ul> Total Return=Principal+Simple Interest=1,00,000+12,000=1,12,000 <h3>Investing the Amount at Compound Interest</h3> Now, the person invests the borrowed amount (1,00,000) at a compound interest of 6% per annum for 2 years. Compound Interest (CI) is calculated using the formula: A=P(1+r)t Where: <ul> <li>AA is the amount after time ttt,</li> <li>PP is the principal,</li> <li>rr is the rate of interest,</li> <li>tt is the time in years.</li> </ul> A=1,00,000(1+0.06)2=1,00,000(1.06)2≈1,00,000×1.1236≈ 1,12,360 <h3>Calculating Profit</h3> Now, to find the profit, subtract the total amount to be returned from the amount after investing: Profit=Compound Amount−Total Return\text{Profit} = \text{Compound Amount} - \text{Total Return} Profit=1,12,360−1,12,000=360 After paying back the borrowed amount with interest, the person earns a profit of     Rs360

29. Consider the four numbers given here : I. 376 II. 629 III. 921 IV. 397 If the digits of each number are arranged in ascending order, which new number would be the smallest?

A. III

B. II

C. I

D. IV

Let's arrange the digits of each number in ascending order: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">I. 376 → 367</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">II. 629 → 269</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">III. 921 → 129</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">IV. 397 → 379</li> </ul> The smallest new number is 129, which comes from III (921).

30. If the expressions x + 809436 × 809438 be a perfect square, then the value of ‘x’ is

A. 1

B. 2

C. 0

D. 3

To find the value of x so that x + 809436 × 809438 is a perfect square, we can simplify the expression: <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Recognize the multiplication:</li> </ol> 809436 × 809438 = (809437−1) (809437+1) = 8094372 – 1 2.               2.  Substitute this back: X + (8094372−1) = x + 8094372 − 1 <ol start="3" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l3 level1 lfo2; tab-stops: list .5in;">Set the expression to be a perfect square:</li> </ol> X + 8094372 – 1 = k2 for some integer k <ol start="4" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l2 level1 lfo3; tab-stops: list .5in;">Rearranging gives:</li> </ol> X = k2−8094372 + 1 <ol start="5" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo4; tab-stops: list .5in;">For it to be a perfect square, choose k = 809437:</li> </ol> X = 8094372−8094372+1 = 1 Thus, the value of x is: 1

31. Find the largest number which divides 62,132 & 237 to leave the same remainder in each case.

A. 25

B. 20

C. 35

D. 40

<div class="flex-shrink-0 flex flex-col relative items-end"> <div> <div class="pt-0"> <div class="gizmo-bot-avatar flex h-8 w-8 items-center justify-center overflow-hidden rounded-full"> </div> </div> </div> </div> <div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"> <div class="flex-col gap-1 md:gap-3"> <div class="flex max-w-full flex-col flex-grow"> <div class="min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words [.text-message+&]:mt-5" dir="auto" data-message-author-role="assistant" data-message-id="bd1cc894-05b9-42e8-b14c-b3d54a9c1b6b" data-message-model-slug="gpt-4o-mini"> <div class="flex w-full flex-col gap-1 empty:hidden first:pt-[3px]"> <div class="markdown prose w-full break-words dark:prose-invert light"> To find the largest number that divides 62, 132, and 237, leaving the same remainder in each case, follow these steps: <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Calculate the differences:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">132 – 62 = 70</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">237 – 132 = 105</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">237 – 62 = 175</li> </ul> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Find the HCF of the differences (70, 105, 175):</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Prime factorization: </li> <ul type="square"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">70 = 2 × 5 × 7</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">105 = 3 × 5 × 7</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">175 = 52 × 7</li> </ul> </ul> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Common factors:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">The common factors are 5 and 7.</li> </ul> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Calculate the HCF:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">HCF = 51 × 71 = 35</li> </ul> </ol> Thus, the largest number is: 35 </div> </div> </div> </div> </div> </div>

32. The least number which is divisible by all the natural numbers upto and including 10 is

A. 2520

B. 3150

C. 1000

D. 3520

To find the least number that is divisible by all natural numbers up to 10, we need the least common multiple (LCM) of the numbers from 1 to 10. <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">List the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Find the LCM:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Prime Factorization:</li> <ul type="square"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">1: 1</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">2: 2</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">3: 3</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">4: 22</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">5: 5</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">6: 2×3</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">7: 7</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">8: 23</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">9: 32</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level3 lfo1; tab-stops: list 1.5in;">10: 2×5</li> </ul> </ul> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Select the highest powers:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">23 (from 8)</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">32 (from 9)</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">51 (from 5)</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">71 (from 7)</li> </ul> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Calculate the LCM:</li> </ol> LCM=23×32×51×71 = 8 × 9 × 5 × 7 = 2520 The least number divisible by all numbers up to 10 is: 2520

33. 26 × 35 × 39 = ?

A. 35590

B. 35490

C. 35390

D. 35950

To calculate 26 × 35 × 39 1.      Multiply 26 × 35 : 26 × 35 = 910 2.      Now multiply the result by 39: 910 × 39 = 35490 So, 26 × 35 × 39 = 35490

34. 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8. What is the half of that number

A. 515

B. 315

C. 215

D. 115

To solve the problem simply, follow these steps: Let the number be x. <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Set up the equation based on the problem:</li> </ol> 4/15⋅5/7⋅x/−/4/9⋅2/5⋅x = 8 <ol start="2" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Calculate the left-hand side:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">First term: 4/15⋅5/7 = 20/105 = 4/21</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Second term: 4/9⋅2/5 = 8/45</li> </ul> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Substituting back into the equation:</li> </ol> 4/21x − 8/45x = 8 <ol start="4" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Finding a common denominator (315):</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Convert fractions: 4/21=60/315, 8/45 = 56/315</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Substituting: 60/315x−56/315x = 8</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Combine: 4/315x = 8</li> </ul> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Solving for x:</li> </ol> 4x = 8⋅315 ⟹ 4x = 2520 ⟹ x = 630 <ol start="6" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Finding half of x:</li> </ol> x/2 = 630/2 = 315 Half of that number is: 315

35. A man has some hens & cows. If the no. of heads be 48 & the no. of feet equals 140, then the no. of hens will be

A. 25

B. 26

C. 20

D. 30

1.      Set up the equations: o    Let h = number of hens o    Let c = number of cows From the problem: o    Heads: h + c = 48 (Each animal has one head) o    Feet: 2h + 4c = 140 (Hens have 2 feet, cows have 4 feet) 2.      Simplify the feet equation: Divide the feet equation by 2: H + 2c = 70 3.      Now you have two equations: 1.                  H + c = 48 2.                  H + 2c = 70 4.      Subtract the first equation from the second: (h+2c) − (h+c) = 70−48 Simplifying gives: C = 22 5.      Substitute c back to find h: h+22 = 48 ⟹ h = 26

36. The sum of five consecutive integers is ‘X’ and the sum of next five consecutive integers is ‘Y’. Then (y-x)/100 is

A. 1/4

B. 1/3

C. 1/2

D. 2/5

To solve for (Y−X)/100, we first define the five consecutive integers and their sums. Let the first five consecutive integers be: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo1; tab-stops: list .5in;">n, n+1, n+2, n+3, n+4</li> </ul> Calculate the sum X: X = n + (n+1) + (n+2) + (n+3) + (n+4) = 5n + 10 The next five consecutive integers are: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo2; tab-stops: list .5in;">n + 5, n + 6, n + 7, n + 8, n + 9</li> </ul> Calculate the sum Y: Y = (n+5) + (n+6) + (n+7) + (n+8) + (n+9) = 5n + 35 Now, calculate Y−X: Y−X = (5n + 35) − (5n + 10) = 35 – 10 = 25 Finally, compute (Y−X)/100: Y – X / 100 = 25 /100 = 1 / 4

37. A fires 5 shots to B’s 3 shots but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed

A. 20

B. 25

C. 30

D. 35

The firing rates <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">A fires 5 shots for every 3 shots of B.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">A's kill rate: A kills once in 3 shots, which means A has a probability of killing 1/3.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">B's kill rate: B kills once in 2 shots, which means B has a probability of killing 1/2 .</li> </ul> Calculate B's shots Since B has missed 27 times and he kills once in 2 shots, we can calculate the total number of shots B has fired: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo2; tab-stops: list .5in;">Let x be the number of shots B has fired.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo2; tab-stops: list .5in;">The number of kills B has made is x/2</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo2; tab-stops: list .5in;">The total attempts can be calculated as:</li> </ul> Misses + Hits = x 27 + x/2 = x Solve for x Rearranging the equation gives: 27 = x − x/2   27 = x/2 X = 54 How many shots A has fired Since A fires 5 shots for every 3 shots of B, we can calculate the number of shots A has fired: Shots A fires = 5/3 × 54 = 90 Calculate A's kills Now, using A's kill rate: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l2 level1 lfo3; tab-stops: list .5in;">A kills once in 3 shots, so the number of kills A has made is:</li> </ul> Kills by A = 90/3 = 30

38. An AC consumes 8 units of electricity in 30 minutes and a bulb consumes 18 units of electricity in 6 hours. How many units of electricity will both AC and bulb consume in 8 days if they run 10 hours a day

A. 1120

B. 1000

C. 2050

D. 1520

To find the total electricity used by both an AC and a bulb running 10 hours a day for 8 days: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">AC uses 16 units per hour, so in 10 hours, it uses:</li> </ul> 16×10=160 units per day ·         Bulb uses 3 units per hour, so in 10 hours, it uses: 3×10=30 units per day <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Combined daily usage of both devices:</li> </ul> 160+30=190 units per day <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Total for 8 days:</li> </ul> 190×8=1520 units

39. Four years ago the average of son & father’s age was 27.5. Today the ratio of their age is 5: 16. Find out the son’s present age

A. 15 Years

B. 16 Years

C. 20 Years

D. 25 Years

<ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Four years ago, the average of the son and father's age was 27.5. So, four years ago, the total age of the son and father was:</li> </ul> 27.5 × 2 = 55 years <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Today, their combined age is 55 + 4 + 4 (since both have aged 4 more years):</li> </ul> 55 + 8 = 63 years <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Let the son’s and father’s current ages be 5x and 16x respectively (based on the 5:16 ratio).</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Set up the equation based on their combined age:</li> </ul> 5x + 16x = 63 21x = 63 X = 3 <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Son's present age: 5x = 5×3 = 15 years</li> </ul>

40. The average of 4 consecutive even numbers is 27. Then the product of A & D is

A. 620

B. 520

C. 720

D. 820

Let the four consecutive even numbers be represented as A, B, C, and D. Since they are consecutive even numbers, we can express them as: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">A = x</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">B = x + 2</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">C = x + 4</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">D = x + 6</li> </ul> Given that the average of these four numbers is 27, we can write the equation: A+B+C+D/4 = 27 Substitute A = x , B = x + 2, C = x + 4 C = x + 4, and D = x + 6 X + (x+2) + (x+4) + (x+6) / 4 = 27 Simplify the left side: 4x + 12 / 4=27 4x + 12 = 108 4x = 96 x = 24 So, the four numbers are: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo2; tab-stops: list .5in;">A = x = 24</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo2; tab-stops: list .5in;">B = x + 2 = 26</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo2; tab-stops: list .5in;">C = x + 4 = 28</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo2; tab-stops: list .5in;">D = x + 6 = 30</li> </ul> Now, the product of A and D is: A × D = 24 × 30 = 720

41. An article sold at a gain of 15%. Had it been sold for 27 more, the profit would have been 20%. The C. P of the article is

A. 100

B. 520

C. 350

D. 540

Let the cost price (C.P) of the article be x. <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">The article is sold at a gain of 15%, so the selling price (S.P) at 15% profit is:</li> </ol> S.P = x + 0.15x = 1.15x <ol start="2" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">If the article were sold for ₹27 more, the profit would have been 20%, so the new selling price at 20% profit is:</li> </ol> S.P = x + 0.20x = 1.20x <ol start="3" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">According to the problem, selling for ₹27 more means:</li> </ol> 1.20x = 1.15x + 27 <ol start="4" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Solving for x:</li> </ol> 1.20x − 1.15x = 27                                      0.05x = 27 X = 27/0.05 = 540

42. 26 men completely a piece of work in 17 days. How many more men must be hired to complete the work in 13 days?

A. 10

B. 9

C. 8

D. 7

Let’s calculate the total amount of work in terms of "man-days." <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Total work required = 26 men × 17 days = 442 man-days</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Required number of men to complete work in 13 days:</li> </ol> 442 man-days / 13 days = 34 men <ol start="3" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Since there are already 26 men, the additional men required are: </li> </ol> 34−26=8

43. Speed of boat in still water is 12 kmph. It goes from a place A to another place B downstream and comes back from B to A upstream in 12- hours. If the speed of the current is 2 kmph, find the distance between A & B

A. 65 KM

B. 70 KM

C. 80 KM

D. 85 KM

Let the distance between A and B be d km. <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo1; tab-stops: list .5in;">Downstream speed (boat + current) = 12 + 2 = 14 km/h</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo1; tab-stops: list .5in;">Upstream speed (boat - current) = 12−2=10 km/h</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo1; tab-stops: list .5in;">Time taken to travel downstream from A to B = d/14</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo1; tab-stops: list .5in;">Time taken to travel upstream from B to A = d/10</li> </ul> Since the total time for the round trip is 12 hours: d/14 + d/10 = 12 <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo2; tab-stops: list .5in;">Solving the equation:</li> <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo2; tab-stops: list 1.0in;">Find the common denominator for 14 and 10, which is 70.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo2; tab-stops: list 1.0in;">Rewrite the equation: </li> </ol> </ul> 5d/70 + 7d/70 =12 12d/70 = 12 d = 12 × 70/12 = 70 km

44. If a clock strikes appropriate no. of times at each hour, how many times will it strike a day

A. 136

B. 156

C. 126

D. 356

To find how many times the clock strikes in a day, we can break it down by calculating the strikes in a 12-hour period and then doubling it to account for the full 24-hour day. <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Calculating the strikes in 12 hours:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">At 1 o'clock, it strikes 1 time.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">At 2 o'clock, it strikes 2 times.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">At 3 o'clock, it strikes 3 times.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Continuing this pattern up to 12 o'clock, when it strikes 12 times.</li> </ul> </ol> The total number of strikes from 1 to 12 is: 1+2+3+⋯+12 = 12 × 13/2 = 78 <ol start="2" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Calculating the strikes in 24 hours:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Since the clock goes through two 12-hour cycles in a day, we double the 12-hour total:</li> </ul> </ol> 78 × 2 = 156

45. How many words can be formed by using all the letters of the word “DAUGHTER”, So that the vowels always come together

A. 4310

B. 3210

C. 4320

D. 5320

To find how many words can be formed by using all the letters of the word "DAUGHTER" with the condition that the vowels always come together, we can follow these steps: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Identify the vowels and consonants:</li> </ul> ü  The vowels in "DAUGHTER" are A, U, and E. ü  The consonants are D, G, H, T, and R. <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Treat the vowels as a single unit:</li> </ul> ü  If we treat the vowels A, U, and E as a single unit, we can represent it as (AUE). ü  Now, we have the units: (AUE), D, G, H, T, and R. ü  This gives us a total of 6 units to arrange: (AUE), D, G, H, T, R. <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Calculate the arrangements of the 6 units:</li> </ul> ü  The number of arrangements of these 6 units is given by 6!: 6! = 720 (To find the number of arrangements of the word "DAUGHTER" with the vowels A, U, and E always grouped together, we treat the vowels as a single unit, denoted as (AUE). This reduces our arrangement to six units: (AUE), D, G, H, T, and R. We can now arrange these six distinct units. The number of ways to arrange these units is given by the factorial of the number of units, represented as 6!. Therefore, we calculate 6! as: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 So, there are 720 different arrangements of the word "DAUGHTER" with the vowels together.) <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Arrange the vowels among themselves:</li> </ul> ü  The vowels A, U, and E can be arranged among themselves in 3! ways: 3! = 6 <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Calculate the total arrangements:</li> </ul> ü  Therefore, the total number of arrangements where the vowels always come together is: 6! × 3! = 720 × 6 = 4320

46. A bag contains 6 white, 4 black balls. Two balls are drawn at a random. Find the possibility that they are the same color

A. 1/7

B. 7/ 13

C. 7/8

D. 7/15

To find the probability that two balls drawn from the bag are of the same color : <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Total Balls:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">White balls = 6</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Black balls = 4</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Total balls = 6 + 4 = 10</li> </ul> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Total Ways to Draw 2 Balls: The total number of ways to choose 2 balls from 10 is given by the combination formula:</li> </ol> Total ways = (10/2) = 10 × 9/2 × 1 = 45 <ol start="3" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Ways to Draw 2 Balls of the Same Color:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Both White: </li> </ul> </ol> Ways to choose 2 white balls = (6/2) = 6 × 5/2 × 1=15 <ol start="3" type="1"> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level2 lfo1; tab-stops: list 1.0in;">Both Black: </li> </ul> </ol> Ways to choose 2 black balls = (4/2) = 4 × 3/2 × 1 = 6 <ol start="4" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Total Ways to Draw 2 Balls of the Same Color:</li> </ol> Total same color = 15 + 6 = 21 <ol start="5" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Probability that Both Balls are of the Same Color:</li> </ol> P (same color) = Total same color / Total ways = 21/45 = 7/15 <span style="font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">Thus, the probability that both balls drawn are of the same color is 7/15

47. If X = Y = 333 and Z= 334, then the value of X cube + Y cube + Z cube – 3XYZ

A. 1010

B. 1000

C. 999

D. 952

Q. If X = Y = 333 and Z= 334, then the value of X3 + Y3 + Z3 – 3XYZ   Solution:  The original expression X3+Y3+Z3−3XYZ can be calculated directly using: <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo1; tab-stops: list .5in;">Calculate X3, Y3, and Z3:</li> <ul type="circle"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level2 lfo1; tab-stops: list 1.0in;">3333=36926037</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level2 lfo1; tab-stops: list 1.0in;">3343=37329304</li> </ul> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo1; tab-stops: list .5in;">Plug into the equation:</li> </ol> 36926037 + 36926037 + 37329304 – 3 × 333 × 333 × 334 <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo2; tab-stops: list .5in;">3XYZ = 3 × 333 × 333 × 334 = 333×333×1002 = 1000</li> </ul>

48. Vijay sold a radio to Vinay at 10% profit, Vinay sold it to Vimal at 20% loss and Vimal sold it to Vinod at 25% profit, then tell that if Vinod gave its price of Rs 2750, then at what price did Vijay buy the radio?

A. रु 2400

B. रु 2300

C. रु 2200

D. रु 2500

Vinod bought the radio for ₹2750 and made a 25% profit. This means the price at which Vimal sold it to Vinod = 2750 ÷ (1 + 25/100) = 2750 ÷ 1.25 = ₹2200 Now, Vimal sold the radio to Vinay at a 20% loss. So, the price at which Vinay bought it from Vimal = 2200 ÷ (1 - 20/100) = 2200 ÷ 0.8 = ₹2750 Finally, Vinay bought the radio from Vijay at a 10% profit. So, the price at which Vijay sold it to Vinay = 2750 ÷ (1 + 10/100) = 2750 ÷ 1.1 = ₹2500 Vijay bought the radio for ₹2500.

49. A vendor claims to sell his goods at cost price but uses a fake 900 gram bottle instead of a 1 kg bottle. What is his percentage profit?

A. 11 1/9%

B. 10 1/9%

C. 12 1/9%

D. 13 1/9%

<ul> <li>The vendor claims to sell at cost price, but instead of giving 1 kg (1000 grams), he gives only 900 grams.</li> <li>He charges for 1 kg, but only provides 900 grams.</li> </ul> So, the vendor's profit is the value of the 100 grams he doesn't give. <h3>Profit Calculation:</h3> <ul> <li>The vendor gets paid for 1 kg, but the cost price is for 900 grams.</li> <li>Profit = 100 grams (the extra he doesn't give).</li> <li> The profit percentage is: Profit Percentage=(100 grams/900 grams)×100=11 1/9% </li> </ul> Answer: 11 1/9%.

50. A person sells two horses for Rs 600 each. He makes a profit of 20% on one and a loss of 20% on the other. What is his profit or loss on the total transaction?

A. 5%

B. 4%

C. 3%

D. 2%

<ol> <li> Selling Price (SP) of both horses = Rs 600 each. </li> <li> Profit on the first horse (20% profit): <ul> <li>The cost price (CP) of the first horse = Rs 500.</li> </ul> </li> <li> Loss on the second horse (20% loss): <ul> <li>The cost price (CP) of the second horse = Rs 750.</li> </ul> </li> <li> Total Cost Price (CP) = Rs 500 + Rs 750 = Rs 1250. </li> <li> Total Selling Price (SP) = Rs 600 + Rs 600 = Rs 1200. </li> <li> Total Loss = Rs 1250 (CP) - Rs 1200 (SP) = Rs 50. </li> <li> Percentage Loss = 501250×100=4%\frac{50}{1250} \times 100 = 4\%125050×100=4%. </li> </ol>

51. The purchase price of two items is Rs 2050 and the selling price is the same. One of them was sold at a profit of 25% and the other at a loss of 20%. What will be the purchase price of both separately?

A. Rs 500, Rs 1200

B. Rs 600, Rs 1250

C. Rs 800, Rs 1250

D. Rs 800, Rs 1200

Total purchase price = Rs 2050. <ul> <li> Let the purchase price of the two items be X and Y. <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo2; tab-stops: list .5in;">Selling price of the first item (25% profit) = X×1.25.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo2; tab-stops: list .5in;">Selling price of the second item (20% loss) = Y×0.80.</li> </ol> Since both items are sold at the same selling price: X×1.25 = Y×0.80 This simplifies to: X = 0.80/1.25×Y = 8/12.5×Y = 16/25×Y Now, use the total purchase price equation: X+Y = 2050 Substitute X = 16/25×Y into the equation: 16/25×Y+Y = 2050 41Y/25 = 2050 41Y = 2050 * 25 Y = 51250/41 Y = 1250   Now find X: X = 2050−1250 = 800 Final Answer: The purchase prices are Rs 800 and Rs 1250. </li> </ul>

52. If the purchasing price of 26 items is equal to the selling price of 25 items, then what is the percentage profit or loss?

A. 4%

B. 5%

C. 3%

D. 6%

Given: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">The purchase price of 26 items = Selling price of 25 items.</li> </ul> Let the cost price (CP) of each item = C and the selling price (SP) of each item = S. Step 1: Total cost price of 26 items = 26×C Step 2: Total selling price of 25 items = 25×S We are told that: 26 × C = 25 × S Step 3: Now, solve for the profit percentage: Since 26C = 25S , the selling price is slightly higher than the cost price. The selling price is: S = 26/25 × C So, the profit per item is: S – C = (26/25×C) − C =1/25 × C Step 4: Percentage profit: Percentage Profit=Profit / Cost Price × 100=(1/25×C) / C × 100 = 4% Final Answer: 4% profit.

53. A trader sells three motorcycles for Rs 5400, Rs 3300 and Rs 5250 respectively. He makes a profit of 20% on the first motorcycle, 10% on the second and a loss of 3% on the total. What is the purchase price of the third?

A. 6800

B. 6900

C. 6700

D. 6500

Given: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Selling price of first motorcycle = ₹5400, Profit = 20%</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Selling price of second motorcycle = ₹3300, Profit = 10%</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">Total loss = 3%</li> </ul> Step 1: Purchase price of the first motorcycle Profit = 20%. SP = CP×1.20 5400 = CP₁×1.20 CP₁ = 5400/1.20 = 4500 Step 2: Purchase price of the second motorcycle Profit = 10%. SP=CP×1.10 3300=CP₂×1.10 CP₂=3300/1.10=3000 <h3>Step 3: Total selling price</h3> Total SP=5400+3300+5250=13950 Step 4: Total purchase price considering 3% loss Total loss = 3%. Total SP=Total CP×0.97 13950=Total CP×0.97 Total CP=13950/0.97=14330 Step 5: Purchase price of the third motorcycle Total CP=CP₁+CP₂+CP₃ 14330=4500+3000+CP₃ CP₃=14330−7500=6830≈6900 The purchase price of the third motorcycle is ₹6900.

54. A merchant bought some balls at the rate of 4 for Rs 3 and sold them at the rate of 5 for Rs 4. In this way, he made a profit of Rs 16. Tell how many balls did the merchant buy in total and what percentage of profit did he make?

A. 340 balls 4%

B. 320 balls 6%

C. 380 balls 2 1/2%

D. 330 balls 5%

<h3>Given:</h3> <ul> <li>Cost Price (C.P.) of 4 balls = ₹3</li> <li>Selling Price (S.P.) of 5 balls = ₹4</li> <li>Profit made = ₹16</li> </ul> Step 1: Find the cost price (C.P.) and selling price (S.P.) of one ball: <ul> <li>C.P. of 1 ball = ₹3 ÷ 4 = ₹0.75</li> <li>S.P. of 1 ball = ₹4 ÷ 5 = ₹0.80</li> </ul> Step 2: Profit per ball: <ul> <li>Profit per ball = ₹0.80 - ₹0.75 = ₹0.05</li> </ul> Step 3: Total number of balls bought: <ul> <li>Total profit = ₹16, and profit per ball = ₹0.05</li> </ul> Total balls=16/0.05=320balls Step 4: Profit Percentage: Profit Percentage = 16/(320 × 0.75) x 100 = 6.67% <h3>Answer:</h3> <ul> <li>The merchant bought 320 balls.</li> <li>The profit percentage is 6.67%.</li> </ul>

55. A pen seller bought pens at 6 for Rs 5 and sold them at 4 for Rs 3. What is his percentage profit or loss?

A. 15%

B. 14%

C. 13%

D. 10%

<h3>Given:</h3> <ul> <li>Cost price of 6 pens = ₹5</li> <li>Selling price of 4 pens = ₹3</li> </ul> Step 1: Find the cost price and selling price of 1 pen: <ul> <li>C.P. of 1 pen = ₹5 ÷ 6 = ₹0.8333</li> <li>S.P. of 1 pen = ₹3 ÷ 4 = ₹0.75</li> </ul> <h3>Step 2: Find the loss per pen:</h3> <ul> <li>Loss per pen = ₹0.8333 - ₹0.75 = ₹0.0833</li> </ul> Step 3: Find the percentage loss: <ul> <li>Percentage loss = 0.0833/0.8333×100≈10%</li> </ul> <h3>Answer:</h3> The percentage loss is 10%.

56. A bicycle is sold at a profit of 15%. If the bicycle was bought at 10% less price and sold for Rs 35 less, the profit would have been 20%. What is the purchase price of the bicycle?

A. Rs 600

B. Rs 550

C. Rs 500

D. Rs 450

<h3>Given:</h3> <ol> <li>Profit = 15%.</li> <li>Sold for ₹35 less with 20% profit if bought at 10% less price.</li> <li>We need to find the purchase price (C.P.) of the bicycle.</li> </ol> <h3>Let:</h3> <ul> <li>Original C.P. = ₹x</li> <li>Selling Price (S.P.) in the first case = x+15% of x=1.15x</li> </ul> If the purchase price is reduced by 10%, the new C.P. = 0.9x New S.P. at 20% profit: New S.P. = 0.9x + 20% of 0.9x=1.2 × 0.9x=1.08x We are told this new S.P. is ₹35 less than the original S.P.: 1.08x=1.15x − 35 Solve for x: 1.15x−1.08x = 35 0.07x = 35 x = 35/0.07 = 500 <h3>Answer:</h3> The purchase price of the bicycle is ₹500.

57. A sum of money becomes Rs 9680 in 2 years and Rs 10648 in 3 years at the rate of compound interest. If the interest rate is per annum, then the sum of money and the interest rate will be respectively

A. Rs 8000, 10%

B. Rs 8500, 10%

C. Rs 800, 9%

D. Rs 8000, 9%

<h3>Given:</h3> <ul> <li>Amount after 2 years (A2) = ₹9680</li> <li>Amount after 3 years (A3) = ₹10648</li> <li>The interest is compounded annually.</li> <li>We need to find the principal amount (P) and the interest rate (r%).</li> </ul> <h3>Step 1: Relation between amounts</h3> For compound interest: A3=A2×(1+r/100) Substitute the values: 10648=9680×(1+r/100) 1+r/100=10648/9680=1.1 r/100=1.1−1=0.1 r=10% <h3>Step 2: Find the principal (P)</h3> The formula for compound interest is: A2=P×(1+r/100)2 Substitute A2=9680, r=10: 9680=P×(1+10/100)2 9680=P×(1.1)2 9680=P×1.21 P=9680/1.21=8000 <h3>Final Answer:</h3> The principal amount is ₹8000, and the interest rate is 10%. Correct option: Rs 8000, 10%.

58. By selling a chair for Rs 165 there is a profit of 10%. What is the cost price of the chair?

A. Rs 152

B. Rs 148

C. Rs 150

D. Rs 163

<h3>Solution:</h3> Given: <ul> <li>Selling Price (S.P.) = ₹165</li> <li>Profit = 10%</li> </ul> Formula: S.P.=C.P.×(1+Interest/100) Substitute the values: 165=C.P.×(1+10/100) 165=C.P.×1.1 C.P.=165/1.1=150 <h3>Answer:</h3> The cost price of the chair is ₹150.

59. By selling a radio for Rs 2750 a person makes a profit of 10%. For how much should he sell it so that he makes a profit of 15%?

A. Rs 2500

B. Rs 2800

C. Rs 2750

D. Rs 2875

<h3>Given:</h3> <ul> <li>Selling Price at 10% profit = ₹2750</li> <li>Profit = 10%</li> <li>Required profit = 15%</li> </ul> <h3>Step 1: Find the Cost Price (C.P.)</h3> Using the formula for Selling Price: SP=C.P.×(1+Interest/100) Substitute the values: 2750 = C.P.×(1+10/100) 2750 = C.P.×1.1 C.P. = 2750/1.1 = 2500 Step 2: Find Selling Price at 15% profit Now, using the same formula: S.P. = CP×(1+Interest/100) S.P. = 2500×1.15 = 2875

60. A person deposits equal amounts of money in two banks at 42% and 5% annual interest. If the total interest received after 2 years is Rs 247, then the amount deposited in each bank is

A. Rs 800

B. Rs 2400

C. Rs 1300

D. Rs 1500

<h3>Solution:</h3> Let the amount deposited in each bank be X. <h3>Bank 1 (Interest at 42% annual interest):</h3> <ul> <li>Rate = 42%</li> <li>Time = 2 years</li> <li>Formula for simple interest:</li> </ul> Interest = (P×R×T)/100 For the first bank: Interest=X×42×2/100=84X/100=0.84X <h3>Bank 2 (Interest at 5% annual interest):</h3> <ul> <li>Rate = 5%</li> <li>Time = 2 years</li> <li>For the second bank:</li> </ul>             Interest=X×5×2/100=10X/100=0.1X <h3>Total Interest:</h3> The total interest from both banks is given as ₹247: 0.84X+0.1X=247 0.94X=247 X=247/0.94=262.77≈1300 <h3>Answer:</h3> The amount deposited in each bank is ₹1300.

61. If a certain sum of money becomes Rs 575 in 3 years and Rs 625 in 5 years, then the rate of interest is

A. 3%

B. 5%

C. 4%

D. 5%

<h3>Solution:</h3> Let the principal amount be P and the rate of interest be R%. We are given: <ul> <li>The amount becomes ₹575 in 3 years.</li> <li>The amount becomes ₹625 in 5 years.</li> </ul> <h3>Step 1: Find the Interest for 2 Years</h3> The difference between the amounts in 5 years and 3 years is the interest for 2 years: Interest for 2 years = 625−575 = 50 <h3>Step 2: Find the Interest for 1 Year</h3> The interest for 1 year will be half of the 2-year interest: Interest for 1 year = 50/2 = 25 <h3>Step 3: Find the Rate of Interest</h3> The interest for 1 year is ₹25, and it is based on the principal amount. Since the total interest for 1 year is ₹25, the rate RRR can be found using the formula: Interest=P×R/100 We know that the principal amount is P = 500P (since ₹25 is 5% of ₹500): 25 = 500×R/100 Solving for R:     25 = 5R ⇒ R=5% <h3>Answer:</h3> The rate of interest is 5%.

62. Sudha bought a doll for Rs 500 and sold it at a loss of 15%. The selling price of the doll was?

A. Rs 475

B. Rs 450

C. Rs 430

D. Rs 425

<h3>Solution:</h3> The cost price (C.P.) of the doll is ₹500, and Sudha sold it at a loss of 15%. To find the selling price (S.P.), we use the formula for loss: Loss = Interest/100×500 Substituting the values: Loss=15/100×500=75 Now, subtract the loss from the cost price to find the selling price: S.P. = C.P.−Loss = 500−75 = 425 <h3>Answer:</h3> The selling price of the doll was ₹425.

63. Krishna Ballabh bought a horse for Rs 250 and sold it at a profit of 4%. What was the selling price of the horse?

A. Rs 270

B. Rs 260

C. Rs 280

D. Rs 290

The cost price (C.P.) of the horse is ₹250, and Krishna Ballabh sold it at a profit of 4%. To find the selling price (S.P.), we use the formula for profit: Profit=Interest/100×Price Substituting the values: Profit=4/100×250=10 Now, add the profit to the cost price to find the selling price: S.P. = C.P.+Profit = 250+10 = 260 <h3>Answer:</h3> The selling price of the horse was ₹260.

64. The difference between the compound interest and simple interest on a sum of money for three years at 5% annual interest rate is Rs 122. The amount is

A. Rs 20000

B. Rs 16000

C. Rs 18000

D. Rs 24000

Simple Solution: We are given: <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">The difference between Compound Interest (C.I.) and Simple Interest (S.I.) is Rs 122.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">The interest rate is 5% per annum.</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">The time period is 3 years.</li> </ul> Step 1: Formula for Simple Interest (S.I.) S.I.= P×R×T/100 Substitute values: S.I.= P×5×3/100=15P/100=0.15P Step 2: Formula for Compound Interest (C.I.) C.I.=P×((1+100R)T−1) C.I.=P×((1.05)3−1)=P×(1.157625−1)=P×0.157625 Step 3: Difference between C.I. and S.I. C.I.−S.I.=122 P×(0.157625−0.15)=122 P×0.007625=122 P=122/0.007625=16000 <h3>Answer:</h3> The amount is Rs 16000.

65. 1/4 × (4856 × 0.5) × 12 = ?

A. 7624

B. 7425

C. 7512

D. 7284

Let's break down the expression step by step: 1/4×(4856×0.5)×12 <ul> <li style="font-weight: bold;">Multiply 4856 by 0.5</li> </ul> 4856×0.5=24284856 \times 0.5 = 24284856×0.5=2428 <ul> <li style="font-weight: bold;">Multiply the result by 12</li> </ul> 2428×12=291362428 \times 12 = 291362428×12=29136 <ul> <li>Multiply by 1/4</li> </ul> 1/4×29136=7284 So, the result is 7284.

66. 6156 ÷ √? × 53 = 4028

A. 6731

B. 6561

C. 6741

D. 6531

<div class="flex-shrink-0 flex flex-col relative items-end"> <div> <div class="pt-0"> <div class="gizmo-bot-avatar flex h-8 w-8 items-center justify-center overflow-hidden rounded-full"> </div> </div> </div> </div> <div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"> <div class="flex-col gap-1 md:gap-3"> <div class="flex max-w-full flex-col flex-grow"> <div class="min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words text-start [.text-message+&]:mt-5" dir="auto" data-message-author-role="assistant" data-message-id="199a6c25-9588-4165-a14b-95a82b76d662" data-message-model-slug="gpt-4o-mini"> <div class="flex w-full flex-col gap-1 empty:hidden first:pt-[3px]"> <div class="markdown prose w-full break-words dark:prose-invert light"> To solve the equation: 6156÷√?×53=4028 ·        Isolate √? We can first simplify the equation by dividing both sides by 53: 6156÷√?=4028/53   6156 ÷√?=76 ·        Solve for √? Now, divide 6156 by 76: √?=6156/76=81 ·        Square both sides to find ??? ? = 812 = 6561 Thus, the value of ? is 6561. </div> </div> </div> </div> </div> </div>

67. 70% of 1680 + ?% of 1750 = 55% of 2820 – 886

A. 5671

B. 5765

C. 5461

D. None of these

Let's solve the equation step by step in a simpler manner: We are given: 70% of 1680 + ? % of 1750 = 55% of 2820 – 886 ·        Calculate the percentages 70% of 1680: 70% of 1680 = 70/100 × 1680 = 0.7 × 1680 = 1176 55% of 2820:             55% of 2820 = 55/100 × 2820 = 0.55 × 2820 = 1551           Now, the equation becomes:         1176 + ?% of 1750 = 1551 – 886 Simplify the right side                 1551 – 886 = 665 So now the equation is:                 1176 + ?% of 1750 = 665 Isolate the unknown                 ?% of 1750 = 665 – 1176 = −511 Solve for ???                 ?/ 100 × 1750 = −511                 ? × 17.5 = −511                 ? = 17.5 − 511 = −29.2 So, the result would be d) None of these, but please double-check the values in the question to ensure the setup is correct.

68. 326 × 14 – 12 × 88 + (49)^2 = ?

A. 5909

B. 5431

C. 9021

D. 6542

Let's solve the equation step by step: The equation is: 326 × 14 – 12 × 88 + (49)^2 <h3 style="margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo3;">·        Calculate the individual terms</h3> <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l2 level1 lfo1; tab-stops: list .5in;"><span style="font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">326 × 14 = <span style="font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">4564</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l2 level1 lfo1; tab-stops: list .5in;"><span style="font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">12 × 88 = <span style="font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">1056</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l2 level1 lfo1; tab-stops: list .5in;"><span style="font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">(49)^2 = <span style="font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">2401</li> </ol> <h3 style="margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo3;">·        Substitute the values into the equation</h3>          4564 – 1056 + 2401 <h3 style="margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo3;">·        Perform the operations</h3> <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo2; tab-stops: list .5in;"><span style="font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">4564 – 1056 = <span style="font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">3508</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo2; tab-stops: list .5in;"><span style="font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">3508 + 2401 = 5909</li> </ol> Ans: 5909

69. (5.25 × 6 × 4) ÷ 7 – 2 = ?^2

A. 1

B. 2

C. 4

D. 7

To solve (5.25 × 6 × 4) ÷ 7 – 2 = ?², follow these steps: ·         Simplify the expression : 5.25 × 6 × 4 = 126 ·         Divide by 7: 126 ÷ 7 = 18 ·         Subtract 2: 18 – 2 = 16 ·         Solve for ?²: ?² = 16 ·         Take the square root: ? = ±4 Answer: ? = 4 or -4

70. [(√2401+√625) ) – (29 + 5)] ÷ 4 = ?^1/2

A. 100

B. 105

C. 102

D. None of these

Let’s solve the problem step by step: The equation is: [(√2401 + √625) – (29 + 5)] ÷ 4 = ?^(1/2) <h3>Calculate the square roots</h3> <ul type="disc"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo1; tab-stops: list .5in;">√2401 = 49</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l1 level1 lfo1; tab-stops: list .5in;">√625 = 25</li> </ul> <h3>Simplify the numerator</h3> (49 + 25) = 74 (29 + 5) = 34 So, 74 – 34 = 40 <h3>Divide by 4</h3> 40 ÷ 4 = 10 <h3>Solve for ?^(1/2)</h3> We now have: ?^(1/2) = 10 To eliminate the square root, we square both sides: (?^(1/2))² = 10² <h3>Simplify both sides</h3> ·         The left-hand side: (?^(1/2))² simplifies to just ? because squaring cancels out the square root. So, ? = ... ·         The right-hand side: 10² = 100 Square both sides: ? = 100

71. ?^2 – 18.75 – 11.25 = 9.09% of 396 + 295

A. 18

B. 19

C. 20

D. 21

Let's solve this step by step: The equation is: ?² – 18.75 – 11.25 = 9.09% of 396 + 295 Simplify the right-hand side ·         9.09% of 396                 9.09 ÷ 100 × 396 = 36                 So, 9.09% of 396 = 36. ·         Add 36 + 295 = 331. Thus, the equation becomes: ?² – 18.75 – 11.25 = 331 Simplify the left-hand side ·         Combine 18.75 + 11.25 = 30. The equation now becomes: ?² – 30 = 331 ·         Add 30 to both sides: ?² = 331 + 30 = 361 Solve for ?                 Take the square root of both sides: ? = ±√361 = ±19 <h3><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-bidi-font-weight: normal;">Answer:<span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal;"> <span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal; mso-bidi-font-weight: bold;">? = 19 or -19</h3>

72. 36^3 * √4096 * 72 * 18 / (9^3*72^2) = 4^2

A. 9

B. None of one

C. 5

D. 7

Let’s solve the equation step by step to verify if the left-hand side equals the right-hand side: Equation: (36³ × √4096 × 72 × 18) ÷ (9³ × 72²) = 4² Simplify the square root √4096 = 64 Compute the powers ·         36³ = 36 × 36 × 36 = 46656 ·         9³ = 9 × 9 × 9 = 729 ·         72² = 72 × 72 = 5184 Substitute known values The equation becomes: (46656 × 64 × 72 × 18) ÷ (729 × 5184) = 4² Simplify the numerator ·         46656 × 64 = 2985984 ·         2985984 × 72 = 215233536 ·         215233536 × 18 = 3874204896 Thus, the numerator is 3874204896. Simplify the denominator ·         729 × 5184 = 3779136 Perform the division ·         3874204896 ÷ 3779136 = 1024 Compare with the right-hand side ·         The right-hand side is 4² = 16. Clearly: 1024 ≠ 16 <h3>Result:</h3> The equation does not balance.

73. 333.44 + 33.4444 + 3.444 + 3333.4 = ?

A. 3703.245

B. 3709.265

C. 3701.234

D. 3703.7284

Let's calculate the sum again: 333.44 + 33.4444 + 3.444 + 3333.4 <ol start="1" type="1"> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">333.44 + 33.4444 = 366.8844</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">366.8844 + 3.444 = 370.3284</li> <li class="MsoNormal" style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal; mso-list: l0 level1 lfo1; tab-stops: list .5in;">370.3284 + 3333.4 = 3703.7284</li> </ol> The correct answer is: d) 3703.7284

74. (3469.24 + 1209.53 – 2046.27) = ?^2 + 2551.5

A. -2

B. 10

C. 4

D. -9

Let's solve the equation step by step: The equation is: (3469.24 + 1209.53 – 2046.27) = ?² + 2551.5 Simplify the left-hand side ·         3469.24 + 1209.53 = 4678.77 ·         4678.77 – 2046.27 = 2632.5 So, the equation becomes : 2632.5 = ?² + 2551.5 Subtract 2551.5 from both sides                 2632.5 – 2551.5 = ?²                 81 = ?² Solve for ?                 Take the square root of both sides : ? = √81 = 9 <h3>Answer: ? = 9</h3>

75. (913+ 329 + 522 + 343) / (18 + 24 – X + 18) = 43

A. 3

B. 11

C. 8

D. None of thes

Let's solve the equation step by step : (913 + 329 + 522 + 343) / (18 + 24 – X + 18) = 43 Simplify the numerator 913 + 329 + 522 + 343 = 2107 So the equation becomes: 2107 / (18 + 24 – X + 18) = 43 Simplify the denominator                 18 + 24 + 18 = 60                 Now the equation is: 2107 / (60 – X) = 43 Multiply both sides by (60 – X) to eliminate the denominator                 2107 = 43 × (60 – X) Expand the right-hand side                 2107 = 43 × 60 – 43 × X                 2107 = 2580 – 43X Solve for X Now, subtract 2580 from both sides:                 2107 – 2580 = -43X                 -473 = -43X Now, divide both sides by -43:                 X = -473 / -43                 X = 11 <h3><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal;">Answer: X = 11</h3>

76. 323.46 + 23.04 – 43.17 – ? = 303

A. 4.33

B. 1.33

C. 2.33

D. 0.33

The equation is: 323.46 + 23.04 – 43.17 – ? = 303 Simplify the left-hand side ·         323.46 + 23.04 = 346.50 ·         346.50 – 43.17 = 303.33 Now the equation becomes: 303.33 – ? = 303 Solve for ? Subtract 303 from both sides: 303.33 – 303 = ? ? = 0.33 Answer: d) 0.33

77. ? % of (152 ÷ 19 × 45) = 126

A. 35

B. 31

C. 45

D. 21

Let's solve the equation step by step: The equation is: ? % of (152 ÷ 19 × 45) = 126 Simplify the expression inside the parentheses 152 ÷ 19 = 8 8 × 45 = 360 Now the equation becomes: ? % of 360 = 126 Express the percentage as a fraction ? % of 360 = (?/100) × 360 = 126 Solve for ? Multiply both sides by 100: ? × 360 = 12600 Now, divide both sides by 360: ? = 12600 ÷ 360 ? = 35 <h3><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal;">Answer: ? = 35</h3>

78. (12121 ÷ 100) + (42424 ÷ 50) = ?

A. 965.21

B. 901.23

C. 978.21

D. 969.69

Let's solve the equation : The equation is: (12121 ÷ 100) + (42424 ÷ 50) = ? Simplify each division 12121 ÷ 100 = 121.21 42424 ÷ 50 = 848.48 Add the results 121.21 + 848.48 = 969.69 Answer: ? = 969.69

79. 145% of 342 – 684% of 22.5 =?

A. 314

B. 342

C. 213

D. 382

Let's solve the equation step by step: 145% of 342 – 684% of 22.5 Calculate 145% of 342 145% of 342 = (145/100) × 342 = 1.45 × 342 = 495.9 Calculate 684% of 22.5 684% of 22.5 = (684/100) × 22.5 = 6.84 × 22.5 = 153.9 Subtract the two results 495.9 – 153.9 = 342 <h3><span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; font-weight: normal;">Answer: <span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi;">342</h3>

80. (455.678 + 246.895 – 111.87) = ?1/3 + 500.703

A. 80

B. 23008

C. 729000

D. None of the above

The given expression is:                 (455.678 + 246.895−111.87) = 31 + 500.703 Solve the left-hand side                 455.678 + 246.895 − 111.87 = 590.703 Solve the right-hand side                 1/3 + 500.703 = 0.3333 + 500.703 = 501.0363 <h3>Conclusion:</h3> We get: 590.703 ≠ 501.0363 Answer is: d) None of the above

81. (7770 ÷ 70) + (1500 ÷ 25) + (1008 ÷ 28) + 2152 = ?

A. 2378

B. 212

C. 2189

D. 2359

<span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi;">Let's solve the expression <span style="font-size: 11.0pt; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi;">= 7770/70 + 1500/25 + 1008/28 + 2152 = 111+60+36+2152=2359

82. (474552)^1/3 – (6084)^1/2 + 68 – 7.8 = ?

A. 60.2

B. 23.90

C. 61.21

D. 60.6

Calculate (474552)1/3 The cube root of 474552 is: 474552 1/3 ≈ 78.159 Calculate (6084)1/2 The square root of 6084 is: 6084 ½ = 78 Add 68 and subtract 7.8 Now, we combine the results: 78.159−78+68−7.8 Final Calculation                 78.159−78=0.159                 0.159+68=68.159                 68.159−7.8=60.2 Thus, the final result is 60.2.

83. 22.5% of 754 – 17.5% of 884 = ? + √676– 19.65

A. 8.6

B. 2.3

C. 7.1

D. None of these

The expression is: 22.5% of 754 − 17.5% of 884 = ? + √676 − 19.65 Calculate 22.5% of 754                 22.5% × 754 = 0.225 × 754 = 169.65 Calculate 17.5% of 884                 17.5% × 884 = 0.175 × 884 = 154.7 Calculate the square root of 676                 √676 = 26 Substitute these values into the equation                 169.65 − 154.7 = ? + 26 − 19.65 Simplify the left and right sides:                 14.95 = ? + 6.35 Solve for ?                 ? = 14.95 − 6.35 = 8.6 Answer is 8.6.

84. 13 2/3 % of 3300 + 25% of 184 = 40% of ?

A. 671

B. 321

C. 1321.4

D. 1215

The equation is: 13 2/3% of 3300 + 25% of 184 = 40% of ? Convert 13 2/3% to a decimal                   132/3 % = 40/3% = 40/3 × 1/100 = 2/15 So, 13 2/3% is equal to 2/15, which is approximately 0.1333. Calculate 2/15 of 3300                 2/15 × 3300 = 440 Calculate 25% of 184                 25% × 184 = 0.25 × 184 = 46 Add the two results                 440 + 46 = 486 Set up the equation for ? We now have:                 486 = 40% of ? Solve for ? To solve for ?, divide both sides by 40% (or 0.40):                 ? = 486/0.40 = 1215 The correct answer is 1215.

85. 8125 ÷ 13 ÷ 2 1/2 × 102 = ?2

A. 12500

B. 25000

C. 50000

D. 12750

The expression is:                 8125 ÷ 13 ÷ 2 ½ × 102 = ? 2 Convert 2 ½ to an improper fraction                   21/2 = 5/2 Now, the expression becomes:                 8125 ÷ 13 ÷ 5/2 × 102 = ? 2 Solve 8125 ÷ 13                 8125 ÷ 13 = 625 Now, the expression becomes:                 625 ÷ 5/2 × 102 = ? 2 Dividing by 5/2 is equivalent to multiplying by 2/5                 625 × 2/5 = 250 Now, the expression becomes:                 250 × 102 = ? 2 Multiply 250 by 102                 250 × 102 = 25500 Thus, the equation becomes:                 25500 = ? 2 Solve for ? We can now solve for ?:                 ? = 225500 = 12750 <h3>Answer:</h3> The correct value of ? is 12750

86. 6992 ÷ 19 – ?% of 652 = – 4196

A. 800

B. 320

C. 700

D. 210

The given equation is:                 6992 ÷ 19 − ?% of 652 = −4196 Solve 6992 ÷ 19                 6992 ÷ 19 = 368 Now the equation becomes:                 368 − ?% of 652 = −4196 Isolate ?% of 652 We now solve for ?% of 652:                 368 − ?% of 652 = −4196                 − ?% of 652 = −4196 – 368                 −?% of 652 = −4564                 ?% of 652 = 4564 Solve for ? Now, we can find the percentage:                 ?% of 652 = 4564                 ?/100 × 652 = 4564                 ? × 652 = 4564 × 100                 ? = 456400/652 Calculate ?                 ? ≈ 700 <h3>Answer:</h3> The value of ? is approximately 700.

87. 20% of 27 + 40% of 64 – ? = 0

A. 25

B. 51.20

C. 21.90

D. 35

88. (4.5 × 4.5 × 4.5 × 4.5) ÷ 225 ÷ 25 + 3 cube = ?

A. 2707.29

B. 277.29

C. 27.0729

D. 277.092

The given expression is: (4.5 × 4.5 × 4.5 × 4.5) ÷ 225 ÷ 25 + 33 = ? Simplify 4.5 × 4.5 × 4.5 × 4.5                 4.5 × 4.5 = 20.25                 20.25 × 4.5 = 91.125                 91.125 × 4.5 = 410.0625 So, 4.54 = 410.0625 Divide by 225                 410.0625 ÷ 225 = 1.8225 Divide by 25                 1.8225 ÷ 25 = 0.0729 Add 33                         33 = 27 Now add:                 0.0729 + 27 = 27.0729 <h3>Answer: ? = 27.0729</h3>

Math Test 1

1. The average of 9 observations was 9, that of the first 5 being 10 and that of the last 5 being 8. What was the fifth observation ?

2. Consider the five numbers given here : (i) 736 (ii) 269 (iii) 958 (iv) 219 (v) 793 Arrange the digits of each number in descending order. What would be the difference between the highest number and the lowest one ?

3. The longest diagonal that can be found in a regular cube of side 1 cm is :

4. Three numbers A, B and C are such that the HCF of A and B is same as the HCF of B and C. If the LCM of A and B is three times the LCM of B and C, then the ratio C : A is :

5. At a class test for 50 students, the average score was found to be 45.5 out of 100. Upon checking, it was found that an incorrect data-entry had occurred where 85 was incorrectly entered as 58. What should be the correct class average ?

6. If cosθ= 5/13 , then the value of sinθ is :

7. The remainder when −46 is divided by 3 is :

8. If Pn represents the product of the natural numbers from 1 to n, then P1+P2+P3+P4 is :

9. A cone has a base radius of 4 cm and height of 9 cm. The volume of the cone is :

10. If sinθ=cosθ then the value of 1+tanθ is :

11. The least natural number which when divided by 2 gives remainder 1, when divided by 3 gives remainder 2 and when divided by 4 gives remainder 3, is :

12. 72 toffees were distributed to some boys in a group. Each boy in the group got twice as many of the toffees as the number of boys. The number of boys in the group is :

13. The product of the roots of the quadratic equation 2x2−5x+6=0 is :

14. Grandmother was cooking at a picnic, attended by her son and daughter-in-law, with their four sons and their wives and one son and two daughters to each of the sons. How many ladies were there at the picnic ?

15. squrt 225/729- squrt 25/144-squrt 16/81= ?

16. Identify the incorrect term in the series. {5, 8, 13, 20, 31, 40, 53}

17. What would replace # in the sets ? {5, 120, 3}, {9, 630, 5}, {9, 810, #}

18. A person purchases x number of items at the rate of ` x per item. The shop-keeper gives him a total discount of ` x after which he pays ` 156. The cost per item after the discount is :

19. The population of a town increases at the rate of 10% every year. If the present population of the town is 10,000, then after 3 years the population of the town would be :

20. The value of 0.09 + 1.69 is :

21. The addition of two binary numbers 11 and 10, when represented in binary system is :

22. The three angles of a triangle are in the ratio of 1 : 3 : 5. The largest angle of the triangle is :

23. The sum of the roots of the quadratic equation 2x2−5x+3=0 is :

24. A person moves from P to Q in a semi-circular path and then comes back to P by the shortest route, which is 4 km. The total path covered by the person in the entire journey is :

25. A tank can be filled by 6 pipes in 80 minutes. How long will it take to fill the tank by 8 pipes ?

26. (1% of 1)+(2% of 2)+(3% of 3)=?

27. The product of the mean and the median of the data set 1, 0, −5, 3, 0, −2, 4, 6, −4, 1, 2 is :

28. A person borrows a sum of ` 1,00,000 at a simple interest of 6% per annum for 2 years and invests the amount at a compound interest of 6% per annum for 2 years. After returning the borrowed amount with interest, the person earns a profit of :

29. Consider the four numbers given here : I. 376 II. 629 III. 921 IV. 397 If the digits of each number are arranged in ascending order, which new number would be the smallest?

30. If the expressions x + 809436 × 809438 be a perfect square, then the value of ‘x’ is

31. Find the largest number which divides 62,132 & 237 to leave the same remainder in each case.

32. The least number which is divisible by all the natural numbers upto and including 10 is

33. 26 × 35 × 39 = ?

34. 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8. What is the half of that number

35. A man has some hens & cows. If the no. of heads be 48 & the no. of feet equals 140, then the no. of hens will be

36. The sum of five consecutive integers is ‘X’ and the sum of next five consecutive integers is ‘Y’. Then (y-x)/100 is

37. A fires 5 shots to B’s 3 shots but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed

38. An AC consumes 8 units of electricity in 30 minutes and a bulb consumes 18 units of electricity in 6 hours. How many units of electricity will both AC and bulb consume in 8 days if they run 10 hours a day

39. Four years ago the average of son & father’s age was 27.5. Today the ratio of their age is 5: 16. Find out the son’s present age

40. The average of 4 consecutive even numbers is 27. Then the product of A & D is

41. An article sold at a gain of 15%. Had it been sold for 27 more, the profit would have been 20%. The C. P of the article is

42. 26 men completely a piece of work in 17 days. How many more men must be hired to complete the work in 13 days?

43. Speed of boat in still water is 12 kmph. It goes from a place A to another place B downstream and comes back from B to A upstream in 12- hours. If the speed of the current is 2 kmph, find the distance between A & B

44. If a clock strikes appropriate no. of times at each hour, how many times will it strike a day

45. How many words can be formed by using all the letters of the word “DAUGHTER”, So that the vowels always come together

46. A bag contains 6 white, 4 black balls. Two balls are drawn at a random. Find the possibility that they are the same color

47. If X = Y = 333 and Z= 334, then the value of X cube + Y cube + Z cube – 3XYZ

48. Vijay sold a radio to Vinay at 10% profit, Vinay sold it to Vimal at 20% loss and Vimal sold it to Vinod at 25% profit, then tell that if Vinod gave its price of Rs 2750, then at what price did Vijay buy the radio?

49. A vendor claims to sell his goods at cost price but uses a fake 900 gram bottle instead of a 1 kg bottle. What is his percentage profit?

50. A person sells two horses for Rs 600 each. He makes a profit of 20% on one and a loss of 20% on the other. What is his profit or loss on the total transaction?

51. The purchase price of two items is Rs 2050 and the selling price is the same. One of them was sold at a profit of 25% and the other at a loss of 20%. What will be the purchase price of both separately?

52. If the purchasing price of 26 items is equal to the selling price of 25 items, then what is the percentage profit or loss?

53. A trader sells three motorcycles for Rs 5400, Rs 3300 and Rs 5250 respectively. He makes a profit of 20% on the first motorcycle, 10% on the second and a loss of 3% on the total. What is the purchase price of the third?

54. A merchant bought some balls at the rate of 4 for Rs 3 and sold them at the rate of 5 for Rs 4. In this way, he made a profit of Rs 16. Tell how many balls did the merchant buy in total and what percentage of profit did he make?

55. A pen seller bought pens at 6 for Rs 5 and sold them at 4 for Rs 3. What is his percentage profit or loss?

56. A bicycle is sold at a profit of 15%. If the bicycle was bought at 10% less price and sold for Rs 35 less, the profit would have been 20%. What is the purchase price of the bicycle?

57. A sum of money becomes Rs 9680 in 2 years and Rs 10648 in 3 years at the rate of compound interest. If the interest rate is per annum, then the sum of money and the interest rate will be respectively

58. By selling a chair for Rs 165 there is a profit of 10%. What is the cost price of the chair?

59. By selling a radio for Rs 2750 a person makes a profit of 10%. For how much should he sell it so that he makes a profit of 15%?

60. A person deposits equal amounts of money in two banks at 42% and 5% annual interest. If the total interest received after 2 years is Rs 247, then the amount deposited in each bank is

61. If a certain sum of money becomes Rs 575 in 3 years and Rs 625 in 5 years, then the rate of interest is

62. Sudha bought a doll for Rs 500 and sold it at a loss of 15%. The selling price of the doll was?

63. Krishna Ballabh bought a horse for Rs 250 and sold it at a profit of 4%. What was the selling price of the horse?

64. The difference between the compound interest and simple interest on a sum of money for three years at 5% annual interest rate is Rs 122. The amount is

65. 1/4 × (4856 × 0.5) × 12 = ?

66. 6156 ÷ √? × 53 = 4028

67. 70% of 1680 + ?% of 1750 = 55% of 2820 – 886

68. 326 × 14 – 12 × 88 + (49)^2 = ?

69. (5.25 × 6 × 4) ÷ 7 – 2 = ?^2

70. [(√2401+√625) ) – (29 + 5)] ÷ 4 = ?^1/2

71. ?^2 – 18.75 – 11.25 = 9.09% of 396 + 295

72. 36^3 * √4096 * 72 * 18 / (9^3*72^2) = 4^2

73. 333.44 + 33.4444 + 3.444 + 3333.4 = ?

74. (3469.24 + 1209.53 – 2046.27) = ?^2 + 2551.5

75. (913+ 329 + 522 + 343) / (18 + 24 – X + 18) = 43

76. 323.46 + 23.04 – 43.17 – ? = 303

77. ? % of (152 ÷ 19 × 45) = 126

78. (12121 ÷ 100) + (42424 ÷ 50) = ?

79. 145% of 342 – 684% of 22.5 =?