Question

Six years ago father was seven times as old as his son . After six years he will be 3 times as old as his son . DEtermine their present ages.

Answer 1

Let the present age of son = x yrs
Let the present age of father = y yrs

6 YEARS AGO :

son's age = (x - 6) yrs
father's age = (y - 6) yrs
​acc. to given condition,
(y - 6) = 7(x - 6)
$\Rightarrow$y - 6 = 7x - 42
$\Rightarrow$y = 7x - 36 ...........(1)

6 YEARS LATER :
son's age = (x + 6) yrs​
father's age = (y + 6) yrs

acc. to given condition,

y + 6 = 3(x + 6)
$\Rightarrow$y = 3x + 12 .......(2)

comparing (1) and (2), we get
7x - 36 = 3x + 12
$\Rightarrow$7x - 3x = 12 + 36
$\Rightarrow$4x = 48
$\Rightarrow$ x = 12

from (1), we get y = 7(12) - 36 = 84 - 36 = 48
so, son's present age = 12 yrs.
father's present age = 48 yrs.