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Free Arithmetic MCQs with Answers

1,060 Arithmetic MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Arithmetic applies numerical operations to percentages, ratios, proportions, profit and loss, averages, and practical rate problems. Questions also involve time, speed and distance, and time and work, requiring careful use of units, direct and inverse relationships, weighted values, and work-rate methods rather than algebraic manipulation.

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1,060 questions · page 32 of 53

621. A bag contains 1 rupee, 2 rupee and 5 rupee coins amounting to Rs.264. If the ratio of the number of these coins is 3:5:4, find the number of 1 rupee coins.

  • A. 66
  • B. 48
  • C. 24
  • D. 8

Explanation: Let the coin counts be 3k, 5k and 4k. Their total value is 1(3k) + 2(5k) + 5(4k) rupees = 33k rupees, so 33k = Rs.264 and k = 8; the…

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Correct answer: 24

622. Divide Rs.2000 into two shares in the ratio 3:2.

  • A. Rs.1200,Rs.800
  • B. Rs.800,Rs.1200
  • C. Rs.1500,Rs.500
  • D. Rs.1100, Rs.900

Explanation: The ratio contains 3 + 2 = 5 parts, so each part is Rs.2000 ÷ 5 = Rs.400. The two shares are 3 × Rs.400 = Rs.1200 and 2 × Rs.400 = Rs.800.

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Correct answer: Rs.1200,Rs.800

623. The ratio of two numbers is 5:9. If each number is decreased by 5, the ratio becomes 5:11. Find the numbers.

  • A. 30, 19
  • B. 21, 37
  • C. 15, 34
  • D. 15, 27Enrolling In Online Certification Courses

Explanation: Let the numbers be 5k and 9k. After decreasing each by 5, (5k − 5):(9k − 5) = 5:11, so 11(5k − 5) = 5(9k − 5), giving k = 3 and numbers 15…

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Correct answer: 15, 27Enrolling In Online Certification Courses

624. The third proportional to 3.5, 5.6 is:___________?

  • A. 8.96
  • B. 8
  • C. 4.5
  • D. 6.2

Explanation: If c is the third proportional to 3.5 and 5.6, then 3.5:5.6 = 5.6:c, so c = 5.6² ÷ 3.5 = 31.36 ÷ 3.5 = 8.96.

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Correct answer: 8.96

625. According to a recipe, 400 grams of flour should be mixed with 500 grams of sugar to bake cookies. If I have only 300 grams of flour, how much sugar should I mix to maintain the same proportion?

  • A. 360
  • B. 380
  • C. 375
  • D. 400

Explanation: The flour-to-sugar ratio is 400 g:500 g = 4:5. For 300 g of flour, the sugar needed is 300 g × 5/4 = 375 g.

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Correct answer: 375

626. X, Y and Z are quantities of the same kind such that X:Y=5:8 and Y:Z=4:7. Find X:Z.

  • A. 32:35
  • B. 67:56
  • C. 5:14
  • D. 5:7

Explanation: Make the two expressions for Y equal: X:Y = 5:8 and Y:Z = 4:7, so multiply the second ratio by 2 to get Y:Z = 8:14.

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Correct answer: 5:14

627. Two kinds of rice, 1st costs Rs.13 per kg and 2nd costs Rs.19 per kg are mixed together. Find the ratio in which the 2 types are mixed so that the mixture costs Rs.14.2 per kg?

  • A. 3:1
  • B. 4:1
  • C. 3:4
  • D. 4:3

Explanation: By alligation, the quantities of Rs.13 rice and Rs.19 rice are in the ratio (19 − 14.2):(14.2 − 13) = 4.8:1.2 = 4:1.

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Correct answer: 4:1

628. A, B, C and D divide a sum of money among themselves in the ratio 7:4:3:2. If D gets Rs. 500 less than A, find the total amount.

  • A. Rs.100
  • B. Rs.700
  • C. Rs.1600
  • D. Rs.2000

Explanation: A and D differ by 7 − 2 = 5 ratio parts, and this difference is Rs.500, so one part is Rs.500 ÷ 5 = Rs.100.

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Correct answer: Rs.1600

629. Solve for x 2x:25 = 6:(x/3)

  • A. 18
  • B. 15
  • C. 12
  • D. 5

Explanation: Interpret the proportion as 2x:25 = 6:(x/3), giving 2x/25 = 6/(x/3) = 18/x. Hence 2x² = 450, so x² = 225 and the positive value is x = 15.

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Correct answer: 15

630. Two natural numbers whose sum is 72 cannot be in the ratio:

  • A. 1:2
  • B. 3:5
  • C. 1:3
  • D. 3:4

Explanation: For a ratio a:b and total 72, the sum of ratio parts must divide 72. Ratios 1:2, 3:5 and 1:3 give integer pairs, but 3:4 has 7 parts and…

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Correct answer: 3:4

631. A journey of 750 km was covered partly by car(x km) and partly by train(y km). If the distance travelled by train was 150 km more than the distance travelled by car, find x:y.

  • A. 2:3
  • B. 3:2
  • C. 3:4
  • D. 4:3

Explanation: Let the car distance be x km, so the train distance is x + 150 km. Then x + x + 150 = 750, giving 2x = 600 and x = 300 km; train distance…

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Correct answer: 2:3

632. The sum of squares of three numbers is 280. If the numbers are in the ratio 3:5:6, find the greatest number.

  • A. 8
  • B. 6
  • C. 12
  • D. 18

Explanation: Let the numbers be 3k, 5k and 6k. Their squared sum is (3k)² + (5k)² + (6k)² = 9k² + 25k² + 36k² = 70k², so 70k² = 280 and k² = 4, giving…

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Correct answer: 12

633. If a flat costs Rs.4500 per sq. ft, and a commercial space costs Rs.9500 per sq. ft, then what is the ratio of their areas if the total cost of both are the same?

  • A. 9:19
  • B. 19:9
  • C. 15:28
  • D. 28:15

Explanation: With equal total costs, 4500 rupees per square foot × flat area = 9500 rupees per square foot × commercial area.

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Correct answer: 19:9

634. The sum of three numbers is 172. The ratio of the first and second numbers is 8:11. The ratio of the second and third is 5:7. Find the second number.

  • A. 44
  • B. 55
  • C. 66
  • D. 77

Explanation: Make the second term common: 8:11 becomes 40:55, while 5:7 becomes 55:77.

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Correct answer: 55

635. 4 singers, 5 dancers and 3 comperes divide an amount of Rs.130000 among themselves such that 3 comperes get as much as 2 dancers and 3 dancers get as much as 2 singers. Find the amount received by a singer.

  • A. Rs.18000
  • B. Rs.13000
  • C. Rs.15000
  • D. Rs.10000

Explanation: Let one singer's share be s. From 3 dancers = 2 singers, one dancer gets 2s/3, and from 3 comperes = 2 dancers, one compere gets 4s/9…

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Correct answer: Rs.15000

636. The sum of cubes of two numbers is 280. If the numbers are in the ratio 2:3, find the smallest number.

  • A. 4
  • B. 6
  • C. 3
  • D. 2

Explanation: Write the numbers as 2k and 3k. Their cubes give (2k)^3 + (3k)^3 = 8k^3 + 27k^3 = 35k^3 = 280, so k^3 = 8 and k = 2; the smaller number is…

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Correct answer: 4

637. Find the value of x when y = 5, if x varies directly as 4y-1 and x = 14 when y = 2.

  • A. 38
  • B. 35
  • C. 10
  • D. 28

Explanation: Direct variation means x = k(4y - 1). Using x = 14 when y = 2 gives 14 = k(8 - 1) = 7k, so k = 2; when y = 5, x = 2(20 - 1) = 38.

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Correct answer: 38

638. The number of seats available for Biology and Computer Science in a school is in the ratio 5:8. They are to be increased by 30% and 25% . Find the new ratio.

  • A. 6:10
  • B. 13:20
  • C. 3:4
  • D. 35:33

Explanation: Take the original numbers as 5k and 8k. After the increases they become 5k(1.30) = 6.5k and 8k(1.25) = 10k, so their ratio is 6.5:10 =…

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Correct answer: 13:20

639. A:B=2:3, B:C=3:4, A:D=4:5. Find C:D.

  • A. 2:5
  • B. 4:5
  • C. 6:5
  • D. 8:5

Explanation: Let A = 2k and B = 3k from A:B = 2:3. Since B:C = 3:4, C = 4k; and A:D = 4:5 gives D = (5/4)(2k) = 5k/2. Therefore C:D = 4k:5k/2 = 8:5.

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Correct answer: 8:5

640. Find the fourth proportion to 3, 7 and 9.

  • A. 63
  • B. 31
  • C. 21
  • D. 27

Explanation: The fourth proportion x satisfies 3:7 = 9:x. Cross-multiplication gives 3x = 7 x 9 = 63, so x = 21.

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Correct answer: 21
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