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30 Ratio & Proportion Questions and Answers

30 solved Ratio & Proportion questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.

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Advanced ratio & proportion questions for experienced learners. These medium-to-hard questions test deeper understanding and are ideal for those who have already mastered the basics. Each question includes a detailed explanation.

Key Formulas

a:b = a/b — ratio compares two quantities If a:b = x:y, then a = kx, b = ky (multiplier method) Proportion: a:b :: c:d means a/b = c/d, cross multiply: ad = bc Sum of parts = (a+b)x, Difference = |a-b|x
Q1 Medium

If A:B = 8:9 and A = 112, what is B?

  • A. 124
  • B. 123
  • C. 126 ✓
  • D. 128
Explanation: Scale factor = 112/8 = 14. So B = 9 x 14 = 126.
Q2 Medium

Simplify the ratio 20:13.

  • A. 19:12
  • B. 21:13
  • C. 20:13 ✓
  • D. 13:20
Explanation: Divide both terms by GCD 1. So 20:13 = 20:13.
Q3 Medium

If A:B = 3:4 and A = 36, what is B?

  • A. 46
  • B. 50
  • C. 48 ✓
  • D. 45
Explanation: Scale factor = 36/3 = 12. So B = 4 x 12 = 48.
Q4 Medium

Two numbers are in the ratio 7:7. If their sum is 140, find the first number.

  • A. 72
  • B. 70 ✓
  • C. 67
  • D. 68
Explanation: When quantities are in a ratio, represent them as multiples of a common variable (x). Then use the given total or difference to find x, and multiply back to get actual values. One part = 140/(14) = 10. First number = 7 x 10 = 70.
Q5 Medium

If A:B = 5:7 and A = 45, what is B?

  • A. 65
  • B. 61
  • C. 60
  • D. 63 ✓
Explanation: Scale factor = 45/5 = 9. So B = 7 x 9 = 63.
Q6 Medium

Two numbers are in the ratio 5:6. If their sum is 143, find the first number.

  • A. 65 ✓
  • B. 63
  • C. 67
  • D. 62
Explanation: When quantities are in a ratio, represent them as multiples of a common variable (x). Then use the given total or difference to find x, and multiply back to get actual values. One part = 143/(11) = 13. First number = 5 x 13 = 65.
Q7 Medium

If A:B = 4:4 and A = 56, what is B?

  • A. 56 ✓
  • B. 58
  • C. 54
  • D. 53
Explanation: Scale factor = 56/4 = 14. So B = 4 x 14 = 56.
Q8 Medium

Simplify the ratio 20:11.

  • A. 19:10
  • B. 11:20
  • C. 21:11
  • D. 20:11 ✓
Explanation: Divide both terms by GCD 1. So 20:11 = 20:11.
Q9 Medium

If A:B = 7:7 and A = 49, what is B?

  • A. 47
  • B. 49 ✓
  • C. 46
  • D. 51
Explanation: Scale factor = 49/7 = 7. So B = 7 x 7 = 49.
Q10 Medium

Simplify the ratio 28:7.

  • A. 21:0
  • B. 4:1 ✓
  • C. 1:4
  • D. 28:7
Explanation: Divide both terms by GCD 7. So 28:7 = 4:1.
Q11 Medium

If A:B = 3:5 and A = 36, what is B?

  • A. 57
  • B. 62
  • C. 60 ✓
  • D. 58
Explanation: Scale factor = 36/3 = 12. So B = 5 x 12 = 60.
Q12 Medium

Two numbers are in the ratio 3:4. If their sum is 140, find the first number.

  • A. 62
  • B. 58
  • C. 57
  • D. 60 ✓
Explanation: When quantities are in a ratio, represent them as multiples of a common variable (x). Then use the given total or difference to find x, and multiply back to get actual values. One part = 140/(7) = 20. First number = 3 x 20 = 60.
Q13 Medium

If A:B = 5:3 and A = 40, what is B?

  • A. 24 ✓
  • B. 22
  • C. 21
  • D. 26
Explanation: Scale factor = 40/5 = 8. So B = 3 x 8 = 24.
Q14 Medium

Simplify the ratio 24:18.

  • A. 18:12
  • B. 24:18
  • C. 4:3 ✓
  • D. 3:4
Explanation: Divide both terms by GCD 6. So 24:18 = 4:3.
Q15 Medium

If A:B = 7:5 and A = 77, what is B?

  • A. 52
  • B. 55 ✓
  • C. 57
  • D. 53
Explanation: Scale factor = 77/7 = 11. So B = 5 x 11 = 55.
Q16 Medium

Two numbers are in the ratio 4:7. If their sum is 220, find the first number.

  • A. 82
  • B. 78
  • C. 77
  • D. 80 ✓
Explanation: When quantities are in a ratio, represent them as multiples of a common variable (x). Then use the given total or difference to find x, and multiply back to get actual values. One part = 220/(11) = 20. First number = 4 x 20 = 80.
Q17 Medium

If A:B = 6:6 and A = 54, what is B?

  • A. 51
  • B. 52
  • C. 56
  • D. 54 ✓
Explanation: Scale factor = 54/6 = 9. So B = 6 x 9 = 54.
Q18 Medium

Simplify the ratio 20:12.

  • A. 3:5
  • B. 5:3 ✓
  • C. 20:12
  • D. 16:8
Explanation: Divide both terms by GCD 4. So 20:12 = 5:3.
Q19 Medium

If A:B = 4:9 and A = 20, what is B?

  • A. 43
  • B. 42
  • C. 45 ✓
  • D. 47
Explanation: Scale factor = 20/4 = 5. So B = 9 x 5 = 45.
Q20 Medium

Two numbers are in the ratio 5:7. If their sum is 72, find the first number.

  • A. 28
  • B. 27
  • C. 30 ✓
  • D. 32
Explanation: When quantities are in a ratio, represent them as multiples of a common variable (x). Then use the given total or difference to find x, and multiply back to get actual values. One part = 72/(12) = 6. First number = 5 x 6 = 30.
Q21 Medium

If A:B = 7:6 and A = 63, what is B?

  • A. 56
  • B. 51
  • C. 54 ✓
  • D. 52
Explanation: Scale factor = 63/7 = 9. So B = 6 x 9 = 54.
Q22 Medium

Simplify the ratio 28:9.

  • A. 9:28
  • B. 28:9 ✓
  • C. 29:9
  • D. 27:8
Explanation: Divide both terms by GCD 1. So 28:9 = 28:9.
Q23 Medium

Two numbers are in the ratio 4:9. If their sum is 195, find the first number.

  • A. 62
  • B. 60 ✓
  • C. 57
  • D. 58
Explanation: When quantities are in a ratio, represent them as multiples of a common variable (x). Then use the given total or difference to find x, and multiply back to get actual values. One part = 195/(13) = 15. First number = 4 x 15 = 60.
Q24 Medium

If A:B = 4:6 and A = 36, what is B?

  • A. 56
  • B. 51
  • C. 54 ✓
  • D. 52
Explanation: Scale factor = 36/4 = 9. So B = 6 x 9 = 54.
Q25 Medium

Two numbers are in the ratio 5:2. If their sum is 98, find the first number.

  • A. 67
  • B. 70 ✓
  • C. 68
  • D. 72
Explanation: When quantities are in a ratio, represent them as multiples of a common variable (x). Then use the given total or difference to find x, and multiply back to get actual values. One part = 98/(7) = 14. First number = 5 x 14 = 70.
Q26 Medium

Simplify the ratio 20:17.

  • A. 21:17
  • B. 17:20
  • C. 20:17 ✓
  • D. 19:16
Explanation: Divide both terms by GCD 1. So 20:17 = 20:17.
Q27 Medium

If A:B = 5:7 and A = 25, what is B?

  • A. 32
  • B. 35 ✓
  • C. 37
  • D. 33
Explanation: Scale factor = 25/5 = 5. So B = 7 x 5 = 35.
Q28 Medium

Two numbers are in the ratio 5:4. If their sum is 144, find the first number.

  • A. 77
  • B. 80 ✓
  • C. 78
  • D. 82
Explanation: When quantities are in a ratio, represent them as multiples of a common variable (x). Then use the given total or difference to find x, and multiply back to get actual values. One part = 144/(9) = 16. First number = 5 x 16 = 80.
Q29 Medium

Simplify the ratio 10:18.

  • A. 10:18
  • B. 5:9 ✓
  • C. 9:5
  • D. 8:16
Explanation: Divide both terms by GCD 2. So 10:18 = 5:9.
Q30 Medium

If A:B = 9:8 and A = 99, what is B?

  • A. 85
  • B. 90
  • C. 86
  • D. 88 ✓
Explanation: Scale factor = 99/9 = 11. So B = 8 x 11 = 88.

Key Takeaways

  • Always introduce a common multiplier (x) when working with ratio problems.
  • Sum of ratio parts × x gives the total; difference of ratio parts × x gives the difference.
  • For compound ratios a:b and b:c: cross-multiply to get a:c.
  • Units must match when comparing through ratios.

Frequently Asked Questions

How do I solve ratio problems?

Let the quantities be expressed as multiples of a common variable. For ratio a:b, let the values = a×x and b×x. Use the given total, sum, or difference to find x, then multiply to get actual values.

What is the difference between ratio and proportion?

A ratio compares two quantities (e.g., a:b). A proportion states that two ratios are equal (e.g., a:b :: c:d, meaning a/b = c/d). In a proportion, cross-multiplying gives ad = bc.

How do I divide a number in a given ratio?

Sum the ratio terms. Each share = Total × (ratio term ÷ sum of ratios). For ratio 2:3:5 with total 100, shares are 20, 30, and 50.

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