Question 1

If x:y = 2:3 and y:z = 6:5, find x:z.

Accepted Answer

Step 1: x:y = 2:3 and y:z = 6:5. Step 2: To make y the same in both ratios, multiply first ratio by 2: x:y = 4:6. Step 3: Now x:y:z = 4:6:5. Step 4: Therefore x:z = 4:5.

Question 2

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

Accepted Answer

Step 1: A:B = 7:5 means A/B = 7/5. Step 2: B:C = 5:3 means B/C = 5/3. Step 3: A/C = (A/B) × (B/C) = (7/5) × (5/3) = 7/3. Step 4: Therefore A:C = 7:3.

Question 3

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 4

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

Accepted Answer

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

Question 5

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. Step 3: Priya's share = 5 × 150 = ₹750.

Question 6

The ratio of length to breadth of a rectangle is 4:3. If the length is 20 cm, what is the breadth?

Accepted Answer

Step 1: Let length = 4x and breadth = 3x. Step 2: Given length = 20 cm, so 4x = 20, therefore x = 5. Step 3: Breadth = 3x = 3 × 5 = 15 cm.

Question 7

If 4 workers can complete a task in 12 days, how many days will 6 workers take to complete the same task (assuming equal work rate)?

Accepted Answer

Step 1: Total work = 4 workers × 12 days = 48 worker-days. Step 2: With 6 workers: Days = 48 ÷ 6 = 8 days.

Question 8

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

Accepted Answer

Step 1: Let A's age = 5x and B's age = 7x. Step 2: Given A = 15, so 5x = 15, which gives x = 3. Step 3: B's age = 7x = 7 × 3 = 21 years.

Question 9

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 10

Three numbers are in the ratio 2:3:5. If their sum is 100, what is the largest number?

Accepted Answer

Step 1: Let the numbers be 2x, 3x, and 5x. Step 2: Sum = 2x + 3x + 5x = 10x = 100. Step 3: x = 10. Step 4: Largest number = 5x = 5 × 10 = 50.

Question 11

The ratio of boys to girls in a class is 4:5. If there are 20 boys, what is the total number of students?

Accepted Answer

Step 1: Boys:Girls = 4:5, and Boys = 20. Step 2: 4x = 20, so x = 5. Step 3: Girls = 5x = 5 × 5 = 25. Step 4: Total = 20 + 25 = 45 students.

Question 12

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, and Flour = 210 grams. Step 2: 7x = 210, so x = 30. Step 3: Sugar = 3x = 3 × 30 = 90 grams.

Question 13

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 shares be 5x, 7x, and 8x respectively. Step 2: Difference between B and A = 7x - 5x = 2x = ₹480. Step 3: Solving, x = ₹240. Step 4: Total sum = 5x + 7x + 8x = 20x = 20 × 240 = ₹4800.

Question 14

Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. Find the larger number.

Accepted Answer

Step 1: Let the numbers be 3x and 5x. Step 2: After increasing by 10: (3x+10):(5x+10) = 5:7. Step 3: Cross-multiply: 7(3x+10) = 5(5x+10). Step 4: 21x + 70 = 25x + 50. Step 5: -4x = -20, so x = 5. Step 6: Larger number = 5x = 5(5) = 25.

Question 15

The ratio of ages of father and son is 7:3. After 6 years, the ratio will be 2:1. What is the father's current age?

Accepted Answer

Step 1: Let father's age = 7x and son's age = 3x. Step 2: After 6 years: (7x+6):(3x+6) = 2:1. Step 3: Cross-multiply: 1(7x+6) = 2(3x+6). Step 4: 7x + 6 = 6x + 12. Step 5: x = 6. Step 6: Father's current age = 7x = 7(6) = 42 years.

Question 16

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

Accepted Answer

Step 1: Let milk = 5x and water = 3x. Step 2: After adding 16 litres of water: 5x:(3x+16) = 5:7. Step 3: Cross-multiply: 7(5x) = 5(3x+16). Step 4: 35x = 15x + 80. Step 5: 20x = 80, so x = 4. Step 6: Milk = 5x = 5(4) = 20 litres.

Question 17

Three containers have liquids in the ratio 2:3:4 by volume. If the second container has 15 litres more than the first, what is the total volume in all three containers?

Accepted Answer

Step 1: Let volumes be 2x, 3x, and 4x. Step 2: Difference between second and first = 3x - 2x = x = 15 litres. Step 3: x = 15. Step 4: Total volume = 2x + 3x + 4x = 9x = 9(15) = 135 litres.

Question 18

A profit of ₹2400 is divided among three partners in the ratio 5:7:12. The third partner's share is how much more than the first partner's share?

Accepted Answer

Step 1: Total parts = 5 + 7 + 12 = 24. Step 2: Value of 1 part = 2400 ÷ 24 = ₹100. Step 3: First partner's share = 5 × 100 = ₹500. Step 4: Third partner's share = 12 × 100 = ₹1200. Step 5: Difference = 1200 - 500 = ₹700.

SSC GD Constable Basic Ratio & Proportion

Basic Ratio & Proportion— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Basic Ratio & Proportion — Practice Questions

60-Second Revision — Basic Ratio & Proportion