The sum of the ages of father and a son presently is 70 years. After 10 years, the son's age is exactly half that of the father. What are their ages now?
1). 45 years, 25 years
2). 50 years, 20 years
3). 47 years, 23 years
4). 50 years, 25 years
Let us take the son's and father's present age as 'x' and 'y'.
It is given that, $x + y = 70$ --------> 1
After $10$ years, son's age will be $(x + 10)$ and father's age will be
$( y + 10)$. It is also given that,
$x + 10 = ( y + 10 )/2$ ----------> 2
From equation 1 we get, $x = 70 - y $
Substituting 'x' in equation 2 we get,
$70 - y + 10 = ( y + 10 )/2$
$2 (70 - y + 10 ) = ( y + 10 )$
$140 - 2y + 20 = y + 10$
Rearranging the equation we get,
$y + 2y = 140 + 20 - 10$
$3y = 160 - 10$
$3y = 150$
$y = 150/ 3$
$y = 50$
Substituting the value of 'y' in eqn 1 we get,
$x + 50 = 70$
$x = 70 - 50$
$x = 20 $
So, son's age is $20$ years and father's age is $50$ years.
The correct option is 2). 50 years ,20 years