Question

The present age of Vijaya's mother is four times the present age of Vijaya. After $6$ years the sum of their ages will be $62$ years. Find their present ages.

Answer 1

Let Vijaya's present age '$x$' years
Then we can make the following table

	Vijaya	Vijaya's mother
Present age	$x$	$4x$
Age after $6$ years	$x+6$	$4x+6$

$\therefore$ Sum of their ages after $6$ years $=(x+6)+(4x+6)$
$=x+6+4x+6$
$5x+12$
But it is given that sum of their ages after $6$ years is $62$
$\Rightarrow$ $5x+12=62$
$5x=62-12$
$5x=50$
$x=\frac{50}{5}=10$
Therefore Present age of Vijaya $=x=10$ years
Present age of Vijaya's mother $=4x=4\times 10=40$ years.