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Free Ratio and Proportion MCQs with Answers

293 Ratio and Proportion MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.

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293 questions · page 6 of 15

101. 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

102. 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

103. 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

104. 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

105. 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

106. 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

107. 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

108. 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

109. 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

110. 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

111. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number ?

  • A. 2 : 5
  • B. 3 : 7
  • C. 5 : 3
  • D. 7 : 3

Explanation: Let the first and second numbers be A and B. The condition 40% of A = two-thirds of B gives 0.4A = 2B/3, so A/B = (2/3)/0.4 = (2/3)/(2/5)…

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Correct answer: 5 : 3

112. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats ?

  • A. 2 : 3 : 4
  • B. 6 : 7 : 8
  • C. 6 : 8 : 9
  • D. None of these

Explanation: Apply each increase to its corresponding ratio term: 5 x 1.40 = 7, 7 x 1.50 = 10.5, and 8 x 1.75 = 14.

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Correct answer: 2 : 3 : 4

113. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

  • A. 50
  • B. 100
  • C. 150
  • D. 200

Explanation: Let the numbers of 25-paisa, 10-paisa and 5-paisa coins be k, 2k and 3k.

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Correct answer: 150

114. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is :__________?

  • A. 2 : 5
  • B. 3 : 5
  • C. 4 : 5
  • D. 6 : 7

Explanation: Let the third number be k. The two numbers are 120% of k and 150% of k, so their ratio is 1.2k:1.5k = 12:15 = 4:5.

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Correct answer: 4 : 5

115. A surn of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share ?

  • A. Rs. 500
  • B. Rs. 1500
  • C. Rs. 2000
  • D. None of these

Explanation: The difference between C and D is 4 - 3 = 1 proportionate part, and this equals Rs.1000.

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Correct answer: Rs. 2000

116. The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is :__________?

  • A. 20
  • B. 30
  • C. 48
  • D. 58

Explanation: Let the first two numbers be 2k and 3k, and the last two be 5m and 8m. Since 3k = 5m, use m = 3t and k = 5t, giving the numbers 10t, 15t…

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Correct answer: 30

117. Three numbers are in the ratio of 3 : 4 : 6 and their product is 1944. The largest of these numbers is :___________?

  • A. 6
  • B. 12
  • C. 18
  • D. None of these

Explanation: Write the numbers as 3k, 4k and 6k. Their product is 3k x 4k x 6k = 72k^3 = 1944, so k^3 = 27 and k = 3; the largest number is 6k = 18.

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Correct answer: 18

118. A car can travel 360km with a ¾ full tank. How many km can it travel with a 2/3 full tank?

  • A. 400
  • B. 320
  • C. 240
  • D. 300

Explanation: Distance is proportional to the amount of fuel when the car's consumption is unchanged.

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Correct answer: 320

119. Atif and Bilal, 110 km apart, start cycling towards each other. If Atif covers a distance of 6 km to Bilal's 5 km, how far will Atif have travelled when they meet?

  • A. 66 km
  • B. 55 km
  • C. 50 km
  • D. 60 km

Explanation: Atif's distance and Bilal's distance are in the ratio 6:5, so Atif covers 6/11 of the total 110 km.

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Correct answer: 60 km

120. 12 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?

  • A. 14
  • B. 15
  • C. 16
  • D. 18

Explanation: The tank's capacity is 12 x 13.5 litres = 162 litres. With 9-litre buckets, the number needed is 162 litres / 9 litres = 18 buckets.

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Correct answer: 18
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