SSC Ratio and Proportion Questions with Answers

Ratio and Proportion is the base of many SSC maths chapters such as partnership, mixture, age, profit and loss and time and work. If your ratio concepts are strong, a large part of arithmetic becomes easy. This practice paper has 30 questions with answers and short solutions, from simple ratios to proportionals, compound ratio and application problems.

Practice Paper at a Glance

What Is Ratio and Proportion? Basic Concept in Simple Words

A ratio compares two quantities of the same kind, written as a : b (or a/b). A proportion says that two ratios are equal, for example a : b = c : d.

• In a ratio a : b, a is the antecedent and b is the consequent.
• Ratios do not have units, so both quantities must be converted into the same unit before comparing.
• In a proportion a : b :: c : d, the first and last terms (a, d) are extremes and the middle terms (b, c) are means. Product of extremes = product of means, so ad = bc.

Formulas and Shortcut Tricks for SSC Ratio and Proportion

• Fourth proportional to a, b, c is (b x c) / a.
• Third proportional to a and b is b^2 / a.
• Mean proportional between a and b is the square root of (a x b).
• Compound ratio of a : b and c : d is ac : bd.
• Duplicate ratio of a : b is a^2 : b^2, triplicate is a^3 : b^3 and sub-duplicate is the square root of a : square root of b.
• Combining ratios: if a : b = 2 : 3 and b : c = 4 : 5, make b equal in both (LCM 12) to get a : b : c = 8 : 12 : 15.
• Sharing a sum in the ratio p : q : r: each share = (sum / (p + q + r)) x its part.
• Componendo and dividendo: if a/b = c/d then (a + b)/(a - b) = (c + d)/(c - d).
• Adding or subtracting the same number from both terms of a ratio: form an equation and cross-multiply.

Set 1: Basic Ratio and Proportion Questions (Q1–Q10)

Q1. Simplify the ratio 48 : 72.
Answer: 2 : 3
Solution: Divide both terms by their HCF 24: 48/24 : 72/24 = 2 : 3.

Q2. Divide Rs 1,200 between A and B in the ratio 3 : 5.
Answer: A = Rs 450 and B = Rs 750
Solution: Total parts = 8. One part = 1,200 / 8 = 150. A = 3 x 150 = 450 and B = 5 x 150 = 750.

Q3. Find x if 4 : 6 = x : 15.
Answer: x = 10
Solution: Cross-multiply: 6x = 4 x 15 = 60, so x = 10.

Q4. Find the fourth proportional to 4, 6 and 10.
Answer: 15
Trick: Fourth proportional = (6 x 10) / 4 = 15.

Q5. Find the third proportional to 9 and 12.
Answer: 16
Trick: Third proportional = 12^2 / 9 = 144 / 9 = 16.

Q6. Find the mean proportional between 4 and 16.
Answer: 8
Trick: Mean proportional = square root of (4 x 16) = square root of 64 = 8.

Q7. If a : b = 2 : 3 and b : c = 4 : 5, find a : b : c.
Answer: 8 : 12 : 15
Solution: Make b equal: a : b = 8 : 12 and b : c = 12 : 15. So a : b : c = 8 : 12 : 15.

Q8. If 3x = 5y, find x : y.
Answer: 5 : 3
Solution: x/y = 5/3, so x : y = 5 : 3.

Q9. Find the ratio of 2 hours to 90 minutes.
Answer: 4 : 3
Solution: 2 hours = 120 minutes. 120 : 90 = 4 : 3.

Q10. Two numbers are in the ratio 5 : 7 and their sum is 144. Find the larger number.
Answer: 84
Solution: Larger number = 144 x 7/12 = 84.

Set 2: Application Questions (Q11–Q20)

Q11. Rs 60,000 is divided among A, B and C in the ratio 2 : 3 : 5. How much does C get?
Answer: Rs 30,000
Solution: C = 60,000 x 5/10 = Rs 30,000.

Q12. The ratio of boys to girls in a school is 7 : 5. If there are 480 students in all, how many are girls?
Answer: 200
Solution: Girls = 480 x 5/12 = 200.

Q13. Two numbers are in the ratio 3 : 4. If 6 is added to each, the ratio becomes 4 : 5. Find the numbers.
Answer: 18 and 24
Solution: (3x + 6)/(4x + 6) = 4/5, so 15x + 30 = 16x + 24 and x = 6. Numbers are 18 and 24.

Q14. If A : B = 2 : 3 and B : C = 5 : 4, find A : C.
Answer: 5 : 6
Solution: A : B = 10 : 15 and B : C = 15 : 12. So A : C = 10 : 12 = 5 : 6.

Q15. The ratio of the ages of a father and his son is 5 : 2 and the sum of their ages is 70 years. What will be the age of the son after 5 years?
Answer: 25 years
Solution: Son = 70 x 2/7 = 20 years. After 5 years = 25 years.

Q16. A mixture of 40 litres contains milk and water in the ratio 7 : 3. How much milk is in the mixture?
Answer: 28 litres
Solution: Milk = 40 x 7/10 = 28 litres.

Q17. The incomes of A and B are in the ratio 4 : 3 and their expenditures are in the ratio 3 : 2. If each saves Rs 800, find the income of A.
Answer: Rs 3,200
Solution: Let incomes be 4x and 3x and expenditures 3y and 2y. 4x - 3y = 800 and 3x - 2y = 800. Solving, x = 800, so A's income = 4 x 800 = Rs 3,200.

Q18. If (a + b) / (a - b) = 7/3, find a : b.
Answer: 5 : 2
Trick: 3(a + b) = 7(a - b), so 3a + 3b = 7a - 7b, 10b = 4a and a : b = 5 : 2.

Q19. The cost of 8 pens is Rs 120. Find the cost of 12 pens.
Answer: Rs 180
Solution: Cost is directly proportional to quantity. 120 x 12/8 = Rs 180.

Q20. 12 workers earn Rs 3,600 in 5 days. How much will 8 workers earn in 9 days at the same rate?
Answer: Rs 4,320
Solution: Earning per worker per day = 3,600 / (12 x 5) = Rs 60. For 8 workers in 9 days = 60 x 8 x 9 = Rs 4,320.

Set 3: Mixed and Advanced Questions (Q21–Q30)

Q21. Two numbers are in the ratio 3 : 5 and their LCM is 150. Find the numbers.
Answer: 30 and 50
Solution: Numbers are 3k and 5k with LCM 15k = 150, so k = 10. Numbers = 30 and 50.

Q22. Find the compound ratio of 2 : 3, 4 : 5 and 3 : 7.
Answer: 8 : 35
Solution: Multiply the antecedents and consequents: (2 x 4 x 3) : (3 x 5 x 7) = 24 : 105 = 8 : 35.

Q23. Find the duplicate ratio of 3 : 4.
Answer: 9 : 16
Solution: Duplicate ratio of a : b is a^2 : b^2 = 9 : 16.

Q24. Rs 1,800 is divided among A, B and C so that A gets 2/3 of B and B gets 3/4 of C. How much does C get?
Answer: Rs 800
Solution: A : B = 2 : 3 and B : C = 3 : 4, so A : B : C = 2 : 3 : 4. C = 1,800 x 4/9 = Rs 800.

Q25. Two numbers are in the ratio 2 : 3 and the difference of their squares is 180. Find the larger number.
Answer: 18
Solution: Numbers are 2x and 3x. 9x^2 - 4x^2 = 5x^2 = 180, so x^2 = 36 and x = 6. Larger number = 18.

Q26. An alloy of copper and zinc has them in the ratio 5 : 4. How much zinc is in 27 kg of the alloy?
Answer: 12 kg
Solution: Zinc = 27 x 4/9 = 12 kg.

Q27. Two numbers are in the ratio 5 : 8. If 5 is subtracted from each, the ratio becomes 4 : 7. Find the smaller number.
Answer: 25
Solution: (5x - 5)/(8x - 5) = 4/7, so 35x - 35 = 32x - 20 and 3x = 15, x = 5. Smaller number = 25.

Q28. If a : b = 3 : 4 and c : d = 2 : 5, find ac : bd.
Answer: 3 : 10
Trick: ac : bd = (3 x 2) : (4 x 5) = 6 : 20 = 3 : 10.

Q29. If x / y = 3/4, find the value of (2x + y) / (2x - y).
Answer: 5
Solution: Take x = 3 and y = 4. (6 + 4) / (6 - 4) = 10 / 2 = 5.

Q30. Find the third proportional to 0.8 and 1.2.
Answer: 1.8
Solution: Third proportional = 1.2^2 / 0.8 = 1.44 / 0.8 = 1.8.

Common Mistakes in Ratio and Proportion

• Not converting both quantities into the same unit before forming a ratio.
• Adding the ratio parts incorrectly when sharing money among three people.
• Using the mean proportional formula without taking the square root.
• Making the middle term different while combining a : b and b : c.
• Forgetting that the ratio has no unit in the final answer.
• Mixing up direct and inverse proportion in word problems.

How to Practice These 30 Questions

1. Revise all the proportional formulas and write them on one page.
2. Solve Set 1 in 6 minutes to build speed.
3. For Set 2, always write the total number of parts before dividing.
4. For Set 3, use equations and double check by putting the numbers back in the ratio.
5. Repeat the paper after seven days and track your time.

Related Topics to Study Next

• Time and Work Questions
• Average Questions
• Mixture and Alligation Questions
• SSC Previous Year Papers

Frequently Asked Questions

What is ratio and proportion?

A ratio compares two quantities of the same kind (a : b). A proportion states that two ratios are equal (a : b = c : d). Many SSC arithmetic chapters are based on these two ideas.

What is the formula for the fourth proportional?

If a : b = c : x, then x = (b x c) / a. This x is called the fourth proportional to a, b and c.

What is the formula for the third proportional?

The third proportional to a and b is b^2 / a, because a : b = b : x.

What is the mean proportional?

The mean proportional between a and b is the square root of (a x b), because a : x = x : b.

How do you divide a quantity in a given ratio?

Add the parts of the ratio to get the total parts, divide the quantity by the total parts to find one part, and multiply by each term of the ratio to get each share.

What is compound ratio?

The compound ratio of a : b and c : d is ac : bd. You multiply the antecedents together and the consequents together.

What is the difference between direct and inverse proportion?

In direct proportion, both quantities increase or decrease together (cost and quantity). In inverse proportion, if one increases the other decreases (speed and time for a fixed distance).

How many ratio and proportion questions come in SSC exams?

Direct questions are one or two per shift, but ratio is used inside partnership, mixture, age, profit and loss and time and work questions, so it matters much more than the direct count.

What is componendo and dividendo?

If a/b = c/d, then (a + b)/(a - b) = (c + d)/(c - d). It is a useful trick when sums and differences of variables are given.

How should I prepare ratio and proportion for SSC exams?

Learn the formulas, practise sharing and age questions, solve one set daily within the time limit and then test yourself with previous year SSC papers.