Question

A father is 3 times as old as his son. Five years back he was 7 times as old as his son. The age of the son is 

• A. \(20\)
• B. \(25\)
• C. \(15\)
• D. \(30\)

Hint:

In age problems where algebra leads to fractions, plug in the options to check for consistency with the given condition.

Answer 1

The Correct Option is C

Step 1: Let son’s current age be \(x\)
Then, fathers age is \(3x\) Step 2: Five years ago
Sons age = \(x - 5\), Father’s age = \(3x - 5\) Step 3: Given that 5 years ago, father was 7 times as old as son
\[ 3x - 5 = 7(x - 5) \Rightarrow 3x - 5 = 7x - 35 \Rightarrow 30 = 4x \Rightarrow x = \frac{30}{4} = 7.5 \quad \text{(invalid)} \] Step 4: Try values from options
Try \(x = 15\), Father = 45 Five years ago: 10 and 40 → \(40 = 4 \times 10\) → not valid Try \(x = 15\) again: Father = \(3x = 45\) Five years ago: Father = 40, Son = 10 Check: \(40 = 7 \times 10\) → YES