Ratio and proportion questions

Aptitude Updated 11 Oct 2026

These ratio and proportion questions are made for SSC, bank, railway and campus placement aptitude tests. The 30 questions on this page cover simplifying ratios, compound and duplicate ratios, dividing an amount in a ratio, fourth, third and mean proportionals, ages, salaries and mixtures, and partnership aptitude questions.

Every question has one correct answer worked out step by step, so you can learn the short method and use it in the exam.

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Ratio basics (easy)

Q1. What is the ratio 45 : 60 in its simplest form?
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Answer: A. 3 : 4
Divide both terms by their HCF, 15: 45/15 = 3 and 60/15 = 4.
Q2. What is the ratio of 75 paise to 3 rupees?
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Answer: C. 1 : 4
Convert to the same unit: 3 rupees = 300 paise. 75 : 300 = 1 : 4.
Q3. What is the compound ratio of 2 : 3, 4 : 5 and 5 : 6?
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Answer: B. 4 : 9
Multiply the first terms and the second terms: (2 x 4 x 5) : (3 x 5 x 6) = 40 : 90 = 4 : 9.
Q4. If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?
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Answer: D. 8 : 12 : 15
Make B the same in both ratios: A : B = 8 : 12 and B : C = 12 : 15, so A : B : C = 8 : 12 : 15.
Q5. What is the duplicate ratio of 3 : 4?
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Answer: D. 9 : 16
The duplicate ratio squares each term: 3 x 3 : 4 x 4 = 9 : 16.
Q6. If a : b = 3 : 5, what is (2a + b) : (a + 2b)?
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Answer: B. 11 : 13
Put a = 3 and b = 5: (6 + 5) : (3 + 10) = 11 : 13.

Dividing an amount in a given ratio

Q7. Rs 2,400 is divided between Ravi and Mohan in the ratio 3 : 5. How much does Mohan get?
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Answer: A. Rs 1,500
Total parts = 8, so one part = 2,400 / 8 = 300. Mohan gets 5 x 300 = Rs 1,500.
Q8. Rs 3,600 is divided among A, B and C in the ratio 2 : 3 : 4. What is C's share?
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Answer: C. Rs 1,600
Total parts = 9 and one part = 400. C gets 4 x 400 = Rs 1,600.
Q9. In a school the ratio of boys to girls is 7 : 5. If there are 150 girls, how many students are there in all?
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Answer: A. 360
5 parts = 150, so 1 part = 30. Total = 12 parts = 360.
Q10. Rs 1,000 is divided between A and B so that A gets two-thirds of what B gets. What is A's share?
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Answer: C. Rs 400
A : B = 2 : 3, so A gets 2/5 of 1,000 = Rs 400.
Q11. A bag has 1 rupee, 50 paise and 25 paise coins in the ratio 2 : 3 : 4. If the total value is Rs 108, how many 50 paise coins are there?
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Answer: B. 72
Let the coins be 2k, 3k and 4k. Their value is 2k x 1 + 3k x 0.5 + 4k x 0.25 = 4.5k = 108, so k = 24 and the 50 paise coins number 3 x 24 = 72.
Q12. Two numbers are in the ratio 4 : 7 and their sum is 132. What is the larger number?
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Answer: D. 84
One part = 132 / 11 = 12. The larger number = 7 x 12 = 84.

Proportion questions

Q13. Find the fourth proportional to 9, 12 and 15.
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Answer: D. 20
9 : 12 = 15 : x, so x = 12 x 15 / 9 = 20.
Q14. What is the mean proportional between 16 and 25?
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Answer: B. 20
Mean proportional = square root of (16 x 25) = square root of 400 = 20.
Q15. What is the third proportional to 8 and 12?
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Answer: A. 18
8 : 12 = 12 : x, so x = 12 x 12 / 8 = 18.
Q16. If 5 : 8 :: x : 24, what is the value of x?
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Answer: C. 15
Product of extremes = product of means: 5 x 24 = 8 x x, so x = 120 / 8 = 15.
Q17. What number must be added to each of 5, 9, 13 and 21 so that the results are in proportion?
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Answer: A. 3
(5 + x)(21 + x) = (9 + x)(13 + x) gives 105 + 26x = 117 + 22x, so 4x = 12 and x = 3. Check: 8 : 12 = 16 : 24.
Q18. If 12 pens cost Rs 180, how much will 20 pens cost at the same rate?
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Answer: C. Rs 300
One pen costs 180 / 12 = Rs 15, so 20 pens cost 20 x 15 = Rs 300.

Ages, salaries and mixtures (medium)

Q19. The ages of two brothers are in the ratio 5 : 7. Six years later the ratio of their ages will be 3 : 4. How old is the elder brother today?
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Answer: B. 42 years
Let the ages be 5x and 7x. (5x + 6) / (7x + 6) = 3 / 4 gives 20x + 24 = 21x + 18, so x = 6 and the elder is 7 x 6 = 42 years.
Q20. The salaries of A and B are in the ratio 3 : 5. If each gets a raise of Rs 4,000, the ratio becomes 2 : 3. What is B's salary before the raise?
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Answer: D. Rs 20,000
3(3x + 4,000) = 2(5x + 4,000) gives 9x + 12,000 = 10x + 8,000, so x = 4,000. B's salary = 5 x 4,000 = Rs 20,000.
Q21. A 60 litre mixture has milk and water in the ratio 7 : 3. How much water must be added to make the ratio 7 : 5?
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Answer: D. 12 litres
Milk = 42 litres and water = 18 litres. For 7 : 5 water must be 42 x 5 / 7 = 30 litres, so add 30 - 18 = 12 litres.
Q22. Two vessels have milk and water in the ratios 3 : 1 and 5 : 3. If equal quantities are mixed, what is the ratio of milk to water in the mixture?
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Answer: B. 11 : 5
Milk = 3/4 + 5/8 = 11/8 and water = 1/4 + 3/8 = 5/8 per unit from each vessel. Ratio = 11 : 5.
Q23. The incomes of P and Q are in the ratio 4 : 3 and their expenses are in the ratio 3 : 2. If each saves Rs 6,000, what is P's income?
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Answer: A. Rs 24,000
4x - 3y = 6,000 and 3x - 2y = 6,000 give x = 6,000 and y = 6,000. P's income = 4 x 6,000 = Rs 24,000.
Q24. The ages of A and B are in the ratio 4 : 5 and their sum is 54 years. How old is B?
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Answer: C. 30 years
One part = 54 / 9 = 6, so B = 5 x 6 = 30 years.

Partnership aptitude questions (hard)

Q25. A and B start a business with Rs 30,000 and Rs 45,000 for the same period. Out of a profit of Rs 25,000, what is B's share?
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Answer: A. Rs 15,000
Capital ratio = 30,000 : 45,000 = 2 : 3. B gets 3/5 of 25,000 = Rs 15,000.
Q26. A invests Rs 20,000 for 12 months and B invests Rs 30,000 for 8 months. In what ratio should the profit be shared?
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Answer: C. 1 : 1
Profit is shared in the ratio of capital x time: 20,000 x 12 = 2,40,000 and 30,000 x 8 = 2,40,000, so the ratio is 1 : 1.
Q27. A starts a business with Rs 40,000. After 4 months B joins with Rs 60,000. Out of a year-end profit of Rs 33,000, what is A's share?
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Answer: B. Rs 16,500
A : B = 40,000 x 12 : 60,000 x 8 = 4,80,000 : 4,80,000 = 1 : 1, so A gets half of 33,000 = Rs 16,500.
Q28. A, B and C invest capital in the ratio 2 : 3 : 5 for 6, 4 and 3 months respectively. What is C's share of a profit of Rs 39,000?
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Answer: D. Rs 15,000
Ratio = 2 x 6 : 3 x 4 : 5 x 3 = 12 : 12 : 15 = 4 : 4 : 5. C gets 5/13 of 39,000 = Rs 15,000.
Q29. A invests Rs 50,000 and B invests Rs 30,000. A also manages the business and first takes 10% of the profit for this. The rest is shared in the ratio of capital. How much does A get in all from a profit of Rs 16,000?
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Answer: D. Rs 10,600
Managing share = 1,600. The remaining 14,400 is shared 5 : 3, so A gets 9,000. A's total = 1,600 + 9,000 = Rs 10,600.
Q30. A invests Rs 25,000 for a full year. B joins for the last 6 months only. If they share the profit equally, how much did B invest?
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Answer: B. Rs 50,000
For equal shares, capital x time must be equal: 25,000 x 12 = B x 6, so B = Rs 50,000.

How to prepare

A ratio compares two quantities of the same kind, so always convert them to the same unit first. When a ratio is given, write the quantities as multiples of one unknown, such as 3x and 5x, and form one equation. To join A : B and B : C, make the common term B equal in both ratios.

In a proportion a : b = c : d, the product of the extremes equals the product of the means (a x d = b x c). The mean proportional of a and b is the square root of ab, and the third proportional is b x b / a. In partnership, profit is shared in the ratio of capital x time, so multiply each partner's money by the number of months it stayed in the business before you divide the profit.

Study tips

Always reduce a ratio to its simplest form before comparing or adding.
Write unknown quantities as 'parts' of the ratio to avoid long algebra.
In partnership questions, find capital x months for each partner first.

Questions people ask

What is the difference between ratio and proportion?

A ratio compares two quantities, such as 3 : 4. A proportion states that two ratios are equal, such as 3 : 4 = 9 : 12.

How do I divide an amount in a given ratio?

Add the terms of the ratio to get the total parts and divide the amount by this total to find one part. Multiply one part by each term to get the shares.

How is profit shared in partnership aptitude questions?

Profit is shared in the ratio of capital multiplied by the time for which it was invested. A working partner may first get a fixed share or salary, and only the rest is shared in that ratio.

What is the mean proportional between two numbers?

The mean proportional between a and b is the square root of a x b. For example, the mean proportional between 4 and 9 is 6.

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