Question

The age of the father 5 years ago was 5 times the age of his son. At present the father's age is 3 times that of his son. What is the present age of the father?

• A. 33 years
• B. 30 years
• C. 45 years
• D. None of these

Hint:

Age problems usually reduce to two linear equations in two unknowns. Write present ages first, then carefully shift time (\(\pm\) years) before forming equations.

Answer 1

The Correct Option is B

Step 1: Define variables for present ages.
Let present ages be: Father \(F\) years, Son \(S\) years.
Given (present): \(F = 3S\). Step 2: Translate the condition from 5 years ago.
Five years ago: Father \(= F-5\), Son \(= S-5\).
Given: \(F - 5 = 5(S - 5)\). Step 3: Substitute the present relation and solve.
Use \(F = 3S\) in \(F - 5 = 5(S - 5)\):
\(3S - 5 = 5S - 25 \Rightarrow 20 = 2S \Rightarrow S = 10\).
\(\Rightarrow F = 3S = 3 \times 10 = 30\). Step 4: Conclude.
The father's present age \(= \boxed{30\ \text{years}}\).