Question

The ratio of the ages of Amit and his father is 2:5. After 4 years, the ratio of their ages will become 3:7. What will be the ratio of their ages after 6 years?

• A. 4:9
• B. 19:43
• C. 13:38
• D. 6:11

Hint:

Use algebraic variables and given ratios to solve age problems step-by-step.

Answer 1

The Correct Option is B

Let the present ages of Amit and his father be \(2x\) and \(5x\), respectively.
After 4 years, their ages will be: \[ 2x + 4 \quad \text{and} \quad 5x + 4 \] Given, \[ \frac{2x + 4}{5x + 4} = \frac{3}{7} \] Cross multiply: \[ 7(2x + 4) = 3(5x + 4) \] \[ 14x + 28 = 15x + 12 \] \[ 15x - 14x = 28 - 12 \] \[ x = 16 \] So present ages: \[ Amit = 2 \times 16 = 32, \quad Father = 5 \times 16 = 80 \] After 6 years, ages: \[ 32 + 6 = 38, \quad 80 + 6 = 86 \] Ratio after 6 years: \[ \frac{38}{86} = \frac{19}{43} \]