Question

The age of a man and his son is in the ratio of 7:2. After 15 years, they would be in the ratio of 2:1, what was the father’s age when his son was born?
A. 25 years
B. 30 years
C. 35 years
D. 42 years

Answer 1

Hint: Let $x$ be the common factor of 7 and 2 in the ratio. From the given ratio, the age of man is $7x$ and the age of the son is $2x$. Then write the age of man and age of son after 15 years and form an equation corresponding to the given conditions. Solve the equation and substitute the value of $x$ to find the present ages of man and his son. The age of the man when his son was born can be calculated by subtracting the present age of son from the present age of the man.

Complete step by step answer:
Let the age of man and his son be $7x$ and $2x$ respectively.
The age of the man after 15 years would be $7x + 15$ and the age of his son after 15 years would be $2x + 15$.
According to the given condition, the age of man and his son after 15 years is 2:1.
Hence, the given condition can be written as,
$7x + 15:2x + 15 = 2:1$
The ratio can also be written in division form as,
$\dfrac{{7x + 15}}{{2x + 15}} = \dfrac{2}{1}$
Cross multiply to derive an equation in $x$.
$
  7x + 15 = 2\left( {2x + 15} \right) \\
  7x + 15 = 4x + 30 \\
 $
On dividing the equation throughout by 3, we get,
$
  3x = 15 \\
  x = 5 \\
$
The present age of son is $2\left( 5 \right) = 10{\text{ years}}$ and the present age of man is $7\left( 5 \right) = 35{\text{ years}}$.
The age of the man when his son was born can be calculated by subtracting the present age of son from the present age of the man.
Thus, the age of man is $35 - 10 = 25{\text{ years}}$
Hence, option A is correct.

Note: Make sure that the equations are formed correctly. Substitute the values of $x$ in the expression of the present age of father $7x$ and not in the expression $7x + 15$ of 15 years later. Then, subtract the present age of the son from the father’s present age.