Question 1

The ratio of ages of Amit and Bhavna is 5:3. If Amit is 20 years older than Bhavna, what is Bhavna's present age?

Accepted Answer

Step 1: Let Amit's age = 5x and Bhavna's age = 3x (from ratio 5:3). Step 2: Given that Amit is 20 years older than Bhavna, so 5x - 3x = 20. Step 3: Solving, 2x = 20, therefore x = 10. Step 4: Bhavna's age = 3x = 3(10) = 30 years.

Question 2

A sum of ₹1200 is divided among three people in the ratio 2:3:5. How much does the person with the largest share receive?

Accepted Answer

Step 1: Total parts = 2 + 3 + 5 = 10. Step 2: Value of one part = 1200 ÷ 10 = 120. Step 3: The largest share corresponds to 5 parts. Step 4: Largest share = 5 × 120 = ₹600.

Question 3

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 4

If 12 kg of rice costs ₹480, what is the cost of 18 kg of rice?

Accepted Answer

Step 1: Cost per kg = 480 ÷ 12 = ₹40 per kg. Step 2: Cost of 18 kg = 18 × 40 = ₹720.

Question 5

Two numbers are in the ratio 4:9. If their sum is 156, find the larger number.

Accepted Answer

Step 1: Let the numbers be 4x and 9x. Step 2: Their sum = 4x + 9x = 13x = 156. Step 3: Solving, x = 156 ÷ 13 = 12. Step 4: The larger number = 9x = 9 × 12 = 108.

Question 6

A sum of money is divided among P, Q, and R in the ratio 2:3:5. If R receives ₹1000, what is the total sum?

Accepted Answer

Step 1: Ratio P:Q:R = 2:3:5. Step 2: Let the parts be 2x, 3x, and 5x respectively. Step 3: R receives 5x = ₹1000, so x = 200. Step 4: Total sum = 2x + 3x + 5x = 10x = 10 × 200 = ₹2000.

Question 7

The ratio of speeds of two cars is 5:7. If the slower car travels 250 km, how far does the faster car travel in the same time?

Accepted Answer

Step 1: Speed ratio = 5:7, so slower car speed is 5x and faster car speed is 7x. Step 2: In the same time, distance is proportional to speed. Step 3: Distance ratio = Speed ratio = 5:7. Step 4: If slower car travels 250 km, then 5 parts = 250 km, so 1 part = 50 km. Step 5: Faster car travels 7 parts = 7 × 50 = 350 km.

Question 8

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

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 9

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 is 7x - 5x = 2x = 18. Step 3: Solving, x = 9. Step 4: The larger number = 7x = 7 × 9 = 63.

Question 10

A sum of money is divided among P, Q, and R in the ratio 4:5:6. If Q receives ₹500, what is the total sum?

Accepted Answer

Step 1: Let the shares be 4x, 5x, and 6x for P, Q, and R respectively. Step 2: Q's share = 5x = 500, so x = 100. Step 3: Total sum = 4x + 5x + 6x = 15x = 15(100) = 1500.

Question 11

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is the sum of their ages?

Accepted Answer

Step 1: Let A's age = 5x and B's age = 7x (from ratio 5:7). Step 2: Given A is 15 years younger than B, so 7x - 5x = 15, which gives 2x = 15, thus x = 7.5. Step 3: A's age = 5(7.5) = 37.5 years, B's age = 7(7.5) = 52.5 years. Step 4: Sum = 37.5 + 52.5 = 90 years.

Question 12

If A:B = 7:5 and B:C = 3:4, what is A:C?

Accepted Answer

Step 1: A:B = 7:5 means A = 7m, B = 5m. Step 2: B:C = 3:4 means B = 3n, C = 4n. Step 3: Since B is common, 5m = 3n, so n = 5m/3. Step 4: C = 4n = 4(5m/3) = 20m/3. Step 5: A:C = 7m : 20m/3 = 21m : 20m = 21:20. Therefore, A:C = 21:20.

Question 13

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 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 14

If x:y = 4:5 and y:z = 2:3, what is x:y:z?

Accepted Answer

Step 1: x:y = 4:5 means x = 4k, y = 5k for some constant k. Step 2: y:z = 2:3 means y = 2m, z = 3m for some constant m. Step 3: Since y is common, 5k = 2m, so m = 5k/2. Step 4: z = 3m = 3(5k/2) = 15k/2. Step 5: x:y:z = 4k : 5k : 15k/2 = 8 : 10 : 15 (multiplying by 2 to clear fractions). Therefore, x:y:z = 8:10:15.

Question 15

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 = 3k₁, B = 4k₁. Step 2: B:C = 5:6 means B = 5k₂, C = 6k₂. Step 3: Since B is common, 4k₁ = 5k₂, so k₁/k₂ = 5/4. Step 4: Let k₁ = 5 and k₂ = 4. Then A = 15, B = 20, C = 24. Step 5: A:B:C = 15:20:24.

Question 16

Two numbers are in the ratio 7:9. If their difference is 8, what is the larger number?

Accepted Answer

Step 1: Let the two numbers be 7x and 9x (from ratio 7:9). Step 2: The larger number is 9x and the smaller is 7x. Step 3: Difference = 9x - 7x = 2x = 8, so x = 4. Step 4: Larger number = 9x = 9(4) = 36.

Question 17

The ratio of boys to girls in a class is 3:2. If there are 24 more boys than girls, how many girls are there?

Accepted Answer

Step 1: Let boys = 3x and girls = 2x (from ratio 3:2). Step 2: Given boys are 24 more than girls, so 3x - 2x = 24. Step 3: x = 24. Step 4: Number of girls = 2x = 2 × 24 = 48. Therefore, there are 48 girls.

Question 18

A mixture contains milk and water in the ratio 5:3. If 16 litres of water is added, the ratio becomes 5:7. How much milk was in the original mixture?

Accepted Answer

Step 1: Original ratio is 5:3, so milk = 5x, water = 3x. Step 2: After adding 16 litres of water: milk = 5x, water = 3x + 16. Step 3: New ratio: 5x:(3x + 16) = 5:7. Step 4: Cross-multiply: 7(5x) = 5(3x + 16) → 35x = 15x + 80 → 20x = 80 → x = 4. Step 5: Milk = 5x = 20 litres.

Question 19

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 ₹600, 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 = 600. Step 3: Solving, x = 300. Step 4: Total sum = 5x + 7x + 8x = 20x = 20(300) = ₹6000.

Question 20

A sum of money is divided among P, Q, and R in the ratio 3:4:5. If R receives ₹600 more than P, what is the total sum?

Accepted Answer

Step 1: Let shares be 3x, 4x, 5x. Step 2: R's share - P's share = 5x - 3x = 2x = 600. Step 3: So x = 300. Step 4: Total sum = 3x + 4x + 5x = 12x = 12(300) = 3600.

Question 21

The ratio of incomes of A and B is 5:4, and the ratio of their expenditures is 3:2. If each saves ₹1600, what is A's income?

Accepted Answer

Step 1: Let incomes be 5x and 4x. Let expenditures be 3y and 2y. Step 2: Savings = Income - Expenditure. For A: 5x - 3y = 1600. For B: 4x - 2y = 1600. Step 3: From equation 1: 5x - 3y = 1600. From equation 2: 4x - 2y = 1600. Step 4: Multiply equation 2 by 3 and equation 1 by 2: 12x - 6y = 4800 and 10x - 6y = 3200. Step 5: Subtract: 2x = 1600, so x = 800. Step 6: A's income = 5x = 4000.

SSC CHSL Basic Ratio & Proportion

SSC CHSL Basic Ratio & Proportion — Past Exam Questions

Basic Ratio & Proportion— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Basic Ratio & Proportion — Practice Questions

60-Second Revision — Basic Ratio & Proportion