Question

After Six years , a man's age will be three times the age of his son and three years ago he was nine times of his son's age. Find the present age of the man. [3 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

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

After six years their age is

$x+6,y+6$

According to given condition,

$x+6=3y+18\dots \dots \left(i\right)$

Three years ago their age is

$x-3,y-3$

According to given condition,

$x-3=9y–27\dots \dots \left(ii\right)$

On solving (i) and (ii) we get,

$x=3y+18-6\Rightarrow x=3y+12$

Substituting value of x in (ii)

$x-3=9y–27$

$3y+12-3=9y–27$

$3y+9=9y–27\Rightarrow y=6$

Now , $x=3y+12$

$x=3\left(6\right)+12\Rightarrow x=30$

$x=30,y=6$

$\therefore$ Present age of father is 30 years and sons age is 6 year.