Question

Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.

Quantity I. 5 years ago the ratio of the ages of A and B was 2 ∶ 3. The ratio will become 5 ∶ 6 after 4 years. What is the present age of A?

Quantity II. 13 years ago the ratio of the ages of A and B was 3 ∶ 4 and 13 years from now it will be 6 ∶ 7. What is the present age of A?

1. Quantity I ≥ Quantity II
2. Quantity I ≤ Quantity II
3. Quantity I < Quantity II
4. Quantity I > Quantity II
5. Quantity I = Quantity II or No relation

Answer 1

Correct Answer - Option 3 : Quantity I < Quantity II

Statement I.

Calculation:

Let age of A and B 5 years ago be 2x and 3x respectively

Present age of A = 2x + 5

Present age of B = 3x + 5

Age of A after 4 years = 2x + 5 + 4 = 2x + 9

Age of B after 4 years = 3x + 5 + 4 = 3x + 9

(2x + 9) ∶ (3x + 9) = 5 ∶ 6

⇒ (2x + 9)/(3x + 9) = 5/6

⇒ 12x + 54 = 15x + 45

⇒ 3x = 9

⇒ x = 3

Present age of A = (2 × 3) + 5 = 11 years

Statement II.

Calculation:

Let age of A and B 13 years ago be 3x and 4x respectively

Present age of A = 3x + 13

Age of A after 13 years = 3x + 13 + 13 = 3x + 26

Present age of B = 4x + 13

Age of B after 13 years = 4x + 13 + 13 = 4x + 26

(3x + 26) ∶ (4x + 26) = 6 ∶ 7

⇒ 21x + 182 = 24x + 156

⇒ 3x = 26

⇒ x = 26/3

Present age of A = (26/3 × 3) + 13 = 39 years

∴ Quantity II > Quantity I