Question

Five years ago, the ratio of Aman's age to his father's age was 1:4, and five years from now, the ratio will be 2:5. What was his father's age when Aman was born?

• A. 28 years
• B. 30 years
• C. 35 years
• D. 32 years

Hint:

For age-related problems, define unknowns carefully and systematically form equations based on the given conditions.

Answer 1

The Correct Option is B

Step 1: Assume Aman's age 5 years ago was \(x\), making his father's age at that time \(4x\).
- Aman's present age = \(x + 5\)
- Father's present age = \(4x + 5\)
- Aman's age 5 years later = \(x + 10\)
- Father's age 5 years later = \(4x + 10\)
Step 2: Applying the given condition: \[ \frac{{Aman's age in 5 years}}{{Father's age in 5 years}} = \frac{2}{5} \] \[ \frac{x + 10}{4x + 10} = \frac{2}{5} \] Cross-multiplying yields: \[ 5(x + 10) = 2(4x + 10) \] \[ 5x + 50 = 8x + 20 \] \[ 50 - 20 = 8x - 5x \] \[ 3x = 30 \quad \Rightarrow \quad x = 10 \] Step 3: Find the father's age when Aman was born:
- Aman's current age = \(x + 5 = 10 + 5 = 15\)
- Father's current age = \(4x + 5 = 40 + 5 = 45\)
- Father's age at Aman's birth = \(45 - 15 = 30\). Final Answer: \[ \boxed{{(2) 30 years}} \]