Question 1

If 6 pens cost ₹90, what is the cost of 10 pens?

Accepted Answer

Step 1: Cost of 1 pen = 90 ÷ 6 = ₹15. Step 2: Cost of 10 pens = 15 × 10 = ₹150.

Question 2

A sum of ₹1200 is divided between Raj and Priya in the ratio 3:5. How much does Priya get?

Accepted Answer

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

Question 3

If A:B = 7:5 and B:C = 5:3, then find A:B:C.

Accepted Answer

Step 1: A:B = 7:5 means A = 7k, B = 5k. Step 2: B:C = 5:3 means B = 5m, C = 3m. Step 3: Since B is common, 5k = 5m, so k = m. Step 4: Therefore A:B:C = 7k:5k:3k = 7:5:3.

Question 4

The ratio of ages of Aman and Bhuvan is 4:5. If Aman is 32 years old, what is Bhuvan's age?

Accepted Answer

Step 1: Let Aman's age = 4x and Bhuvan's age = 5x. Step 2: Given Aman = 32, so 4x = 32, therefore x = 8. Step 3: Bhuvan's age = 5x = 5 × 8 = 40 years.

Question 5

In a mixture, the ratio of milk to water is 7:2. If the mixture contains 28 litres of milk, how many litres of water are in the mixture?

Accepted Answer

Step 1: Let milk = 7x and water = 2x. Step 2: Given milk = 28, so 7x = 28, therefore x = 4. Step 3: Water = 2x = 2 × 4 = 8 litres.

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 common factor be x. Boys = 5x, Girls = 3x. Step 2: Given boys = 40, so 5x = 40, therefore x = 8. Step 3: Girls = 3x = 3 × 8 = 24.

Question 7

If 15 kg of rice costs ₹450, what is the cost of 25 kg of rice at the same rate?

Accepted Answer

Step 1: Find cost per kg = 450 ÷ 15 = ₹30 per kg. Step 2: Cost of 25 kg = 25 × 30 = ₹750.

Question 8

In a mixture, the ratio of milk to water is 7:3. If the mixture contains 21 litres of milk, how many litres of water are in the mixture?

Accepted Answer

Step 1: Let milk = 7x and water = 3x (from ratio 7:3). Step 2: Given milk = 21 litres, so 7x = 21. Step 3: x = 3. Step 4: Water = 3x = 3 × 3 = 9 litres.

Question 9

If A:B = 3:5 and B:C = 2:3, find A:B:C.

Accepted Answer

Step 1: A:B = 3:5 means A = 3k, B = 5k for some constant k. Step 2: B:C = 2:3 means B = 2m, C = 3m for some constant m. Step 3: Since B is common, equate: 5k = 2m, so m = 5k/2. Step 4: C = 3m = 3 × (5k/2) = 15k/2. Step 5: To eliminate fractions, multiply all by 2: A = 6, B = 10, C = 15. Therefore A:B:C = 6:10:15.

Question 10

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is A's current age?

Accepted Answer

Step 1: Let A's age = 5x and B's age = 7x (from ratio 5:7). Step 2: Given that A is 15 years younger than B, so 7x - 5x = 15. Step 3: 2x = 15, therefore x = 7.5. Step 4: A's age = 5x = 5 × 7.5 = 37.5 years.

Question 11

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

Accepted Answer

Step 1: Total parts in ratio 2:3:5 = 2 + 3 + 5 = 10 parts. Step 2: Total sum = ₹1200. Step 3: Value of 1 part = 1200 ÷ 10 = ₹120. Step 4: Z receives 5 parts = 5 × 120 = ₹600.

Question 12

The ratio of boys to girls in a school is 4:5. If there are 144 boys, how many total students are in the school?

Accepted Answer

Step 1: Let boys = 4x and girls = 5x (from ratio 4:5). Step 2: Given boys = 144, so 4x = 144. Step 3: x = 36. Step 4: Girls = 5x = 5 × 36 = 180. Step 5: Total students = 144 + 180 = 324.

Question 13

Two quantities A and B are in the ratio 5:8. If A is increased by 40% and B is decreased by 25%, the new ratio becomes A':B'. What is the ratio A':B'?

Accepted Answer

Step 1: Let A = 5k and B = 8k. Step 2: A' = A + 40% of A = 5k + 0.4(5k) = 5k(1.4) = 7k. Step 3: B' = B - 25% of B = 8k - 0.25(8k) = 8k(0.75) = 6k. Step 4: New ratio A':B' = 7k:6k = 7:6.

Question 14

Three numbers are in the ratio 2:3:4. If the sum of the largest and smallest numbers is 90, what is the sum of all three numbers?

Accepted Answer

Step 1: Let the three numbers be 2x, 3x, and 4x. Step 2: Sum of largest and smallest = 4x + 2x = 6x = 90. Step 3: Therefore, x = 15. Step 4: The three numbers are 30, 45, and 60. Step 5: Sum of all three = 30 + 45 + 60 = 135.

Question 15

A sum of money is divided among A, B, and C in the ratio 5:7:8. If the difference between the shares of B and A is ₹480, what is the total sum of money?

Accepted Answer

Step 1: Let the shares be 5x, 7x, and 8x respectively. Step 2: Difference between B and A = 7x - 5x = 2x = ₹480. Step 3: Therefore, x = ₹240. Step 4: Total sum = 5x + 7x + 8x = 20x = 20 × 240 = ₹4,800.

Question 16

In a mixture, the ratio of milk to water is 7:5. If 24 litres of water is added, the ratio becomes 7:9. How many litres of milk was in the original mixture?

Accepted Answer

Step 1: Let milk = 7x and water = 5x litres. Step 2: After adding 24 litres of water: milk = 7x, water = 5x + 24. Step 3: New ratio: 7x/(5x+24) = 7/9. Step 4: Cross-multiply: 9(7x) = 7(5x+24). Step 5: 63x = 35x + 168. Step 6: 28x = 168, so x = 6. Step 7: Milk = 7x = 7(6) = 42 litres.

Question 17

A bag contains red, blue, and green balls in the ratio 4:5:6. If there are 60 more green balls than red balls, how many blue balls are in the bag?

Accepted Answer

Step 1: Let red, blue, and green balls be 4x, 5x, and 6x respectively. Step 2: Difference between green and red = 6x - 4x = 2x = 60. Step 3: Therefore, x = 30. Step 4: Blue balls = 5x = 5(30) = 150.

Question 18

The ratio of ages of two brothers is 3:5. After 6 years, their ages will be in the ratio 2:3. What is the sum of their current ages?

Accepted Answer

Step 1: Let current ages be 3x and 5x. Step 2: After 6 years, ages will be (3x+6) and (5x+6). Step 3: According to the condition: (3x+6)/(5x+6) = 2/3. Step 4: Cross-multiply: 3(3x+6) = 2(5x+6). Step 5: 9x + 18 = 10x + 12. Step 6: x = 6. Step 7: Current ages are 18 and 30. Sum = 48 years.

SSC CPO Basic Ratio & Proportion

SSC CPO Basic Ratio & Proportion — Past Exam Questions

Basic Ratio & Proportion— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Basic Ratio & Proportion