Question

10 years ago the age of a man was 5 years more than four times the age of his son. 10 years hence the age of the man will be 5 years more than 2 times the age of his son. The present age of the man is:

• A. 45 years
• B. 40 years
• C. 55 years
• D. 50 years

Hint:

For age-related problems, define the present ages as variables and set up equations based on given conditions.

Answer 1

The Correct Option is C

Step 1: Define the variables
Let the present age of the man be \( M \) and that of his son be \( S \).
Step 2: Formulate equations based on given conditions
- 10 years ago: \[ M - 10 = 4(S - 10) + 5 \] \[ M - 10 = 4S - 40 + 5 \] \[ M - 10 = 4S - 35 \] \[ M = 4S - 25 \] - 10 years hence: \[ M + 10 = 2(S + 10) + 5 \] \[ M + 10 = 2S + 20 + 5 \] \[ M + 10 = 2S + 25 \] \[ M = 2S + 15 \] Step 3: Solve for \( M \) and \( S \)
Equating both equations: \[ 4S - 25 = 2S + 15 \] \[ 4S - 2S = 15 + 25 \] \[ 2S = 40 \] \[ S = 20 \] Substituting \( S = 20 \) in \( M = 4S - 25 \): \[ M = 4(20) - 25 = 80 - 25 = 55 \] Thus, the correct answer is 55 years.