Question

Six years hence, a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is

• A. $28$ years
• B. $30$ years
• C. $32$ years
• D. $34$ years

Answer 1

Answer: (B)

$30$ years

Let the present age of man be $x$ years and the present age of son be $y$ years

After six years:
Man's age = $(x+6)years$

Son's age = $(y+6)years$

According to the condition
$\Rightarrow x+6=3(y+6)$

$\Rightarrow x-3y=12$

$\Rightarrow x=12+3y$ $...\left(1\right)$

Three years ago:
Man's age =$(x-3)years$
Son's age = $(y-3)years$

According to the condition
$\Rightarrow x-3=9(y-3)$
$\Rightarrow x-9y=-24$ $...\left(2\right)$

Put the value of $x$ in equation $\left(2\right)$
$\Rightarrow 12+3y-9y=-24$

$\Rightarrow y=6$

Put the value of $y$ in equation $\left(1\right)$
$x-3\times 6=12$

$\Rightarrow x=30$

So, Man's age = 30 years