Question 1

If 3 pens cost ₹45, how much will 7 pens cost?

Accepted Answer

Step 1: Cost of 1 pen = ₹45 ÷ 3 = ₹15. Step 2: Cost of 7 pens = 7 × ₹15 = ₹105.

Question 2

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 3

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

Accepted Answer

Step 1: A:B = 7:5 means A = 7k₁, B = 5k₁. Step 2: B:C = 5:3 means B = 5k₂, C = 3k₂. Step 3: For consistency, B must be the same in both ratios. Since B = 5k₁ = 5k₂, we have k₁ = k₂. Step 4: Therefore A:B:C = 7:5:3.

Question 4

The ratio of ages of Ravi and Priya is 4:5. If Ravi is 24 years old, what is Priya's age?

Accepted Answer

Step 1: Let Ravi's age = 4x and Priya's age = 5x. Step 2: Given Ravi's age = 24, so 4x = 24, therefore x = 6. Step 3: Priya's age = 5x = 5 × 6 = 30 years.

Question 5

A sum of money is divided between Arun and Bhavna in the ratio 3:2. If Arun gets ₹600, what is the total sum?

Accepted Answer

Step 1: Let Arun's share = 3x and Bhavna's share = 2x. Step 2: Given Arun's share = ₹600, so 3x = 600, therefore x = 200. Step 3: Total sum = 3x + 2x = 5x = 5 × 200 = ₹1000.

Question 6

The ratio of length to breadth of a rectangle is 5:3. If the breadth is 12 cm, what is the length?

Accepted Answer

Step 1: Let length = 5x and breadth = 3x. Step 2: Given breadth = 12 cm, so 3x = 12, therefore x = 4. Step 3: Length = 5x = 5 × 4 = 20 cm.

Question 7

The ratio of boys to girls in a class is 7:5. If there are 84 boys, how many total students are in the class?

Accepted Answer

Step 1: Boys:Girls = 7:5, so 7x = 84 (boys). Step 2: Solving, x = 12. Step 3: Girls = 5x = 5 × 12 = 60. Step 4: Total students = 84 + 60 = 144.

Question 8

If A:B = 2:3 and B:C = 4:5, and A = 16, find the value of C.

Accepted Answer

Step 1: From A:B = 2:3, we get B = (3/2) × A = (3/2) × 16 = 24. Step 2: From B:C = 4:5, we get C = (5/4) × B = (5/4) × 24 = 30.

Question 9

A mixture contains milk and water in the ratio 5:3. If the mixture contains 40 litres of milk, how many litres of water are in the mixture?

Accepted Answer

Step 1: Milk:Water = 5:3, so 5x = 40 (milk). Step 2: Solving, x = 8. Step 3: Water = 3x = 3 × 8 = 24 litres.

Question 10

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

Accepted Answer

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

Question 11

The ratio of ages of Arun and Bhavna is 5:7. If Arun is 20 years old, what is Bhavna's age?

Accepted Answer

Step 1: Let Arun's age = 5x and Bhavna's age = 7x. Step 2: Given Arun is 20 years old, so 5x = 20, which gives x = 4. Step 3: Bhavna's age = 7x = 7 × 4 = 28 years.

Question 12

The ratio of ages of A, B, and C is 4:5:6. If the sum of their ages is 90 years, what is the difference between the ages of C and A?

Accepted Answer

Step 1: Let the ages be 4x, 5x, and 6x respectively. Step 2: Sum = 4x + 5x + 6x = 15x = 90, so x = 6. Step 3: Age of A = 4(6) = 24 years, Age of C = 6(6) = 36 years. Step 4: Difference = 36 - 24 = 12 years.

Question 13

The ratio of three numbers is 2:3:4. If the sum of the largest and smallest is 90, what is the middle number?

Accepted Answer

Step 1: Let the numbers be 2x, 3x, and 4x. Step 2: Largest + Smallest = 4x + 2x = 6x = 90. Step 3: x = 15. Step 4: Middle number = 3x = 3(15) = 45.

Question 14

In a school, the ratio of boys to girls is 7:5. If 35 more boys join the school, the ratio becomes 12:5. How many girls are in the school?

Accepted Answer

Step 1: Let boys = 7x and girls = 5x. Step 2: After 35 boys join: (7x+35):5x = 12:5. Step 3: 5(7x+35) = 12(5x) → 35x + 175 = 60x → 175 = 25x → x = 7. Step 4: Girls = 5x = 5(7) = 35.

Question 15

A sum of money is divided among P, Q, and R in the ratio 3:7:5. If Q receives ₹2100 more than P, what is the total sum?

Accepted Answer

Step 1: Let the shares be 3x, 7x, and 5x. Step 2: Q's share - P's share = 7x - 3x = 4x = 2100. Step 3: x = 525. Step 4: Total = 3x + 7x + 5x = 15x = 15(525) = 7875.

Question 16

Two numbers are in the ratio 5:8. If each number is increased by 12, the ratio becomes 7:10. Find the larger number.

Accepted Answer

Step 1: Let the numbers be 5x and 8x. Step 2: After increasing by 12: (5x+12):(8x+12) = 7:10. Step 3: 10(5x+12) = 7(8x+12) → 50x + 120 = 56x + 84 → 6x = 36 → x = 6. Step 4: Larger number = 8x = 8(6) = 48.

Question 17

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 is 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: 7(5x) = 5(3x+16) → 35x = 15x + 80 → 20x = 80 → x = 4. Step 4: Milk = 5x = 5(4) = 20 litres.

SSC MTS 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