Three years ago, the ratio of the age of father to that of his son was 8 : 3. After 4 years, their ages will be in the ratio 11 : 5. What
is the present age (in years) of the father.
This questions was previously asked in
SSC CGL 18th April 2022 Shift-3
Explanation:
- Let's denote the father's age three years ago as \( 8x \) and the son's age three years ago as \( 3x \).
- After three years, the father's age will be \( 8x + 3 + 4 = 8x + 7 \) and the son's age will be \( 3x + 3 + 4 = 3x + 7 \).
- We are told that after these four more years, the age ratio becomes 11:5.
- Setting up the equation, \(\frac{8x + 7}{3x + 7} = \frac{11}{5}\).
- Solving gives \(5(8x + 7) = 11(3x + 7)\).
- This simplifies to \(40x + 35 = 33x + 77\).
- Simplifying further, \(7x = 42\) gives \(x = 6\).
- Thus, the present age of the father is \(8x + 3\), which equals \(51\).
- Option 1: 52 - Incorrect, slightly above the calculated age.
- Option 2: 51 - Correct. This matches our calculation.
- Option 3: 48 - Incorrect, below the calculated age.
- Option 4: 55 - Incorrect, above the calculated age.
- The correct answer is Option 2: 51.
.