Two years ago deepak was three times as old as his son and two years hence twice his age will be equal to five times the age of the son. Find their present ages


Given :

Two years ago Deepak was three times as old as his son and two years hence twice his age will be equal to five times the age of the son.

To find :

We have to find the present ages of father and son.

Solution : 

Let the present ages of the son and Deepak be $x$ and $y$ respectively.

This implies,

Age of the son after 2 years $= x+2$

Age of the father after 2 years $= y+2$.

Age of the son 2 years ago $= x-2$.

Age of the father 2 years ago $= y-2$.

Therefore,

$2(y+2) = 5(x+2)$

$2y+4 = 5x+10$

$2y = 5x+10-4$

$y = \frac{5x+6}{2}$.....(i)

$y-2=3(x-2)$

$y-2=3x-6$

$y=3x-6+2$

$\frac{5x+6}{2}=3x-4$    (From (i))

$5x+6=2(3x-4)$

$5x+6=6x-8$

$6x-5x=6+8$

$x=14$

$\Rightarrow y=\frac{5(14)+6}{2}$

$=\frac{70+6}{2}$

$=\frac{76}{2}$

$=38$

The present age of the son is $14$ years and the present age of Deepak is $38$ years.  

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Updated on: 10-Oct-2022

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