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:
\[2x + 4 \text{ and } 5x + 4\]
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:
\[Amit = 2 \times 16 = 32, Father = 5 \times 16 = 80\]
After 6 years, ages:
\[32 + 6 = 38, 80 + 6 = 86\]
Ratio after 6 years:
\[\frac{38}{86} = \frac{19}{43}\]