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Ratio and proportion practice questions for bank exams
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A ratio compares two quantities of the same kind, and a proportion says that two ratios are equal. These questions come in many disguises in bank exams: sharing money, comparing incomes, and ratios that change when something is added. The method is the same each time. Give each quantity a multiple of a common unit k, turn the story into an equation in k, and solve. Try the five questions below.
Terms and tools
| Term | Meaning | Example |
|---|---|---|
| Ratio a : b | a ÷ b | 3 : 4 is three-quarters |
| Proportion | a : b = c : d, so a × d = b × c | 2 : 3 = 4 : 6 |
| Mean proportional of a and b | √(a × b) | 4 and 9 give 6 |
| Third proportional to a and b | b² ÷ a | 4 and 6 give 9 |
| Chain ratio | Equalise the common term | A : B = 3 : 4 and B : C = 6 : 7 |
| Duplicate ratio | a² : b² | 2 : 3 becomes 4 : 9 |
Five practice questions
Question 1
₹7,200 is divided among A, B and C in the ratio 2 : 3 : 4. How much does the person with the largest share get?
- A. ₹2,400
- B. ₹3,200
- C. ₹3,600
- D. ₹4,000
Question 2
If A : B = 3 : 4 and B : C = 6 : 7, what is A : B : C?
- A. 3 : 4 : 7
- B. 9 : 8 : 7
- C. 18 : 12 : 14
- D. 9 : 12 : 14
Question 3
The incomes of A and B are in the ratio 5 : 4 and their expenditures are in the ratio 4 : 3. If each person saves ₹1,000, what is A's income?
- A. ₹4,000
- B. ₹4,500
- C. ₹5,000
- D. ₹5,500
Question 4
Three numbers are in the ratio 2 : 3 : 5, and the sum of their squares is 1,368. What is the largest number?
- A. 24
- B. 30
- C. 36
- D. 42
Question 5
The ratio of boys to girls in a school is 7 : 5. When 20 more girls join, the ratio becomes 7 : 6. How many boys are there in the school?
- A. 100
- B. 120
- C. 140
- D. 160
Answers and explanations
- B. The ratio parts add up to 2 + 3 + 4 = 9, so one part is 7,200 ÷ 9 = 800. The largest share is 4 × 800 = ₹3,200.
- D. B must be the same in both ratios. Multiply the first ratio by 3 to get 9 : 12, and the second by 2 to get 12 : 14. Then A : B : C = 9 : 12 : 14.
- C. Let incomes be 5k and 4k and expenditures 4m and 3m. Then 5k − 4m = 1,000 and 4k − 3m = 1,000. Multiply the first by 3 and the second by 4: 15k − 12m = 3,000 and 16k − 12m = 4,000. Subtract to get k = 1,000. A's income is 5k = ₹5,000.
- B. Let the numbers be 2k, 3k and 5k. The sum of squares is 4k² + 9k² + 25k² = 38k² = 1,368, so k² = 36 and k = 6. The largest number is 5 × 6 = 30.
- C. Let boys be 7k and girls 5k. After 20 girls join, 7k ÷ (5k + 20) = 7 ÷ 6. Cross-multiply: 42k = 35k + 140, so k = 20. Boys are 7 × 20 = 140. Check: girls become 120, and 140 : 120 = 7 : 6.
How to prepare ratio and proportion
- Always introduce k. Writing 5k and 4k keeps the ratio fixed while you solve for the actual size.
- Find what stays constant. In Question 3, savings are equal. In Question 5, the number of boys does not change. The constant quantity is what gives you the equation.
- Equalise the common term in chain ratios by multiplying each ratio by the other's matching term, as in Question 2.
- Use the unitary idea for sharing. Add the parts, find one part, then multiply. Check that your shares add up to the total.
- Expect ratio inside other topics. Ages, mixtures, partnership and profit and loss all depend on it. See ages next, where the ratio changes with time.
- Verify by substitution. Putting the answer back into the original story takes 10 seconds and removes silly errors.
Aim for about 40 seconds on straight sharing and chain-ratio questions. Two-variable sets like Question 3 are mains-level and may take 90 seconds, so attempt them after the quick ones.
The full ratio and proportion topic test is on PrepMatic (about 15 questions, 30 minutes). The Quantitative Aptitude guide shows how this topic fits the section, and the bank exam hub links each exam's pattern.
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