Question

The sum of the present ages of father and his son is 60 years 6 years ago father's age was five times the age of the son After six years son's age will be

• A. 20 years
• B. 14 years
• C. 12 years
• D. 18 years

Answer 1

The correct option is A 20 years

Let the age of father be x and age of son be y.
As per question, $x+y=60$................eq(1)
Six years ago age of father was 5 times sons age so we can derive the following equation.
$(x-6)=5(y-6)$
$\Rightarrow x-5y=-30+6$
$\Rightarrow x-5y=-24$..............eq(2)
To eliminate y term we can multiply eq(1) with 5...thus we get.
$5x+5y=300$
On adding eq(1) and eq(2) we get......$5x+5y=300$
$x-5y=-24$
_________________________
6x=276
x=46
putting value of x in eq (i) we get y=14
after six years son's age will be$(14+6)=20$ years