Question 1

P and Q start a business with investments in the ratio 5:7. At the end of the year, the profit earned is ₹14,400. If P's profit share is ₹6,000, find Q's profit share.

Accepted Answer

Step 1: Investment ratio P:Q = 5:7. Step 2: Profit ratio = Investment ratio = 5:7. Step 3: If P's share is ₹6,000 and corresponds to 5 parts, then 1 part = 6,000 ÷ 5 = ₹1,200. Step 4: Q's share = 7 × 1,200 = ₹8,400.

Question 2

X, Y, and Z form a partnership with capital contributions in the ratio 3:4:5. If the total profit at the end of the year is ₹24,000, what is Z's profit share?

Accepted Answer

Step 1: Capital ratio X:Y:Z = 3:4:5. Step 2: Profit is distributed in the same ratio as capital. Step 3: Total parts = 3 + 4 + 5 = 12. Step 4: Z's share = (5/12) × 24,000 = ₹10,000.

Question 3

A and B enter into a partnership. A invests ₹12,000 and B invests ₹18,000. After one year, the profit is ₹9,000. What is A's share of the profit?

Accepted Answer

Step 1: In a partnership, profit is divided in the ratio of capital invested. Step 2: Ratio of A's investment to B's investment = 12,000 : 18,000 = 2 : 3. Step 3: Total parts = 2 + 3 = 5. Step 4: A's share = (2/5) × 9,000 = ₹3,600.

Question 4

Two containers have sugar solutions of concentrations 20% and 50% respectively. In what ratio should they be mixed to get a solution of 35% concentration?

Accepted Answer

Step 1: Use alligation method. Concentration of solution 1 = 20%, solution 2 = 50%, desired = 35%. Step 2: Difference from desired: 35 - 20 = 15 (for 20% solution), 50 - 35 = 15 (for 50% solution). Step 3: Ratio = 15:15 = 1:1.

Question 5

Three partners A, B, and C invest ₹15,000, ₹20,000, and ₹25,000 respectively. The profit at the end of the year is ₹12,000. How much more profit does C receive compared to A?

Accepted Answer

Step 1: Capital ratio A:B:C = 15,000 : 20,000 : 25,000 = 3 : 4 : 5. Step 2: Profit ratio = Capital ratio = 3 : 4 : 5. Step 3: Total parts = 3 + 4 + 5 = 12. Step 4: A's share = (3/12) × 12,000 = ₹3,000. Step 5: C's share = (5/12) × 12,000 = ₹5,000. Step 6: Difference = 5,000 - 3,000 = ₹2,000.

Question 6

The ratio of boys to girls in a class is 5:3. If there are 40 boys, how many girls are there in the class?

Accepted Answer

Step 1: Let the ratio be 5x:3x where boys = 5x and girls = 3x. Step 2: Given boys = 40, so 5x = 40, which gives x = 8. Step 3: Number of girls = 3x = 3 × 8 = 24.

Question 7

Two numbers are in the ratio 7:5. If their difference is 18, what is the larger number?

Accepted Answer

Step 1: Let the numbers be 7x and 5x. Step 2: Their difference = 7x - 5x = 2x = 18. Step 3: Solving, x = 9. Step 4: Larger number = 7x = 7 × 9 = 63.

Question 8

If A:B = 3:4 and B:C = 5:6, what is A:B:C?

Accepted Answer

Step 1: A:B = 3:4 means A = 3k, B = 4k for some k. Step 2: B:C = 5:6 means B = 5m, C = 6m for some m. Step 3: Since B is common, 4k = 5m, so k/m = 5/4. Step 4: Let k = 5, m = 4. Then A = 15, B = 20, C = 24. Step 5: A:B:C = 15:20:24.

Question 9

A sum of ₹1200 is divided among X, Y, and Z in the ratio 2:3:5. How much does Y receive?

Accepted Answer

Step 1: Total parts = 2 + 3 + 5 = 10. Step 2: Y's share = (3/10) × 1200 = 3 × 120 = 360.

Question 10

If 12 workers can complete a job in 8 days, how many days will 16 workers take to complete the same job?

Accepted Answer

Step 1: Total work = 12 workers × 8 days = 96 worker-days. Step 2: With 16 workers, days required = 96 ÷ 16 = 6 days.

Question 11

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg in the ratio 3:2. What is the cost price per kg of the mixture?

Accepted Answer

Step 1: Rice type 1 costs ₹40/kg, quantity ratio = 3 parts. Rice type 2 costs ₹60/kg, quantity ratio = 2 parts. Step 2: Total cost = (40 × 3) + (60 × 2) = 120 + 120 = 240. Step 3: Total quantity = 3 + 2 = 5 parts. Step 4: Cost per kg = 240/5 = ₹48/kg.

Question 12

A solution contains acid and water in the ratio 2:3. If 10 litres of water is added to 50 litres of this solution, what is the new ratio of acid to water?

Accepted Answer

Step 1: Original solution = 50 litres, ratio acid:water = 2:3, total parts = 5. Acid = (2/5) × 50 = 20 litres, Water = (3/5) × 50 = 30 litres. Step 2: After adding 10 litres of water: Acid = 20 litres (unchanged), Water = 30 + 10 = 40 litres. Step 3: New ratio = 20:40 = 1:2.

Question 13

The ratio of speeds of two cars is 4:5. If the slower car travels 240 km, how far does the faster car travel in the same time?

Accepted Answer

Step 1: Speed ratio = 4:5, so slower car speed = 4k and faster car speed = 5k. Step 2: In the same time, distance is proportional to speed. Step 3: Distance ratio = Speed ratio = 4:5. Step 4: If slower car travels 240 km, then 4 parts = 240, so 1 part = 60. Step 5: Faster car travels 5 parts = 5 × 60 = 300 km.

Question 14

In a partnership, M and N contribute capital in the ratio 4:5. After one year, M receives ₹12,000 as profit. What is the total profit if N's share is to be calculated?

Accepted Answer

Step 1: Capital ratio M:N = 4:5. Step 2: Profit ratio = Capital ratio = 4:5. Step 3: If M's profit (4 parts) = ₹12,000, then 1 part = 12,000 ÷ 4 = ₹3,000. Step 4: N's profit (5 parts) = 5 × 3,000 = ₹15,000. Step 5: Total profit = 12,000 + 15,000 = ₹27,000.

Question 15

A and B enter into a partnership with capital in the ratio 5:7. After 4 months, A adds ₹20,000 to his capital. If A's capital was initially ₹50,000, what is B's initial capital?

Accepted Answer

Step 1: A's initial capital = ₹50,000. Step 2: Ratio of initial capital A:B = 5:7. Step 3: If A's capital is 5 parts and equals ₹50,000, then 1 part = 50,000/5 = ₹10,000. Step 4: B's initial capital = 7 parts = 7 × 10,000 = ₹70,000.

Question 16

The speeds of two cars are in the ratio 5:8. If the slower car travels 250 km in a certain time, how far does the faster car travel in the same time?

Accepted Answer

Step 1: Speed ratio = 5:8 (slower:faster). Step 2: In the same time, distance is proportional to speed. Step 3: Distance ratio = 5:8. Step 4: If slower car travels 250 km (5 parts), then 1 part = 50 km. Step 5: Faster car travels 8 parts = 8 × 50 = 400 km.

Question 17

A sum of ₹1200 is divided between X and Y in the ratio 3:5. How much does Y receive?

Accepted Answer

Step 1: Total parts = 3 + 5 = 8. Step 2: Y's share = (5/8) × 1200. Step 3: Y's share = 5 × 150 = ₹750.

Question 18

A recipe requires flour and sugar in the ratio 7:3. If 210 grams of flour is used, how much sugar (in grams) is needed?

Accepted Answer

Step 1: Flour:Sugar = 7:3. Step 2: Flour = 210 grams = 7 parts, so 1 part = 30 grams. Step 3: Sugar = 3 parts = 3 × 30 = 90 grams.

Question 19

Two containers have alcohol and water in ratios 3:2 and 4:1 respectively. If 20 litres from the first container and 30 litres from the second are mixed together, what is the ratio of alcohol to water in the final mixture?

Accepted Answer

Step 1: Container 1 has ratio 3:2 (total parts = 5). In 20L: alcohol = 20 × (3/5) = 12L, water = 20 × (2/5) = 8L. Step 2: Container 2 has ratio 4:1 (total parts = 5). In 30L: alcohol = 30 × (4/5) = 24L, water = 30 × (1/5) = 6L. Step 3: Final mixture: alcohol = 12 + 24 = 36L, water = 8 + 6 = 14L. Step 4: Ratio = 36:14 = 18:7.

Question 20

A shopkeeper mixes two types of rice costing ₹40 per kg and ₹60 per kg. If the mixture costs ₹50 per kg and the quantity of the first type is 30 kg, find the quantity of the second type.

Accepted Answer

Step 1: Use alligation method. Cost of type 1 = ₹40, cost of type 2 = ₹60, mixture cost = ₹50. Step 2: Difference from type 1: 50 - 40 = 10. Difference from type 2: 60 - 50 = 10. Step 3: Ratio of quantities = 10:10 = 1:1. Step 4: If type 1 = 30 kg, then type 2 = 30 kg.

IBPS Clerk Ratio & Proportion Questions

IBPS Clerk Ratio & Proportion — Past Exam Questions

Study by Subtopic — Ratio & Proportion

Study Next — Quantitative Aptitude Topics