Ten years later, A will be twice as old as B and five years ago, A was three times as old as B. What are the present ages of A and B?


Given :

Ten years later, A will be twice as old as B and five years ago, A was three times as old as B.

To do :

We have to find the present ages of A and B.

Solution :

Let the ages of A and B be $x$ and $y$ respectively.

This implies,

Age of A after 10 years $= x+10$ years.

Age of B after 10 years $= y+10$ years.

Age of A 5 years ago $= x-5$ years.

Age of B 5 years ago $= y-5$ years.

According to the question,

$x+10=2(y+10)$

$x+10=2y+20$

$x=2y+20-10$

$x=2y+10$.....(i)

$x-5=3(y-5)$

$x-5=3y-15$

$3y=(2y+10)+15-5$     (From (i))

$3y=2y+10+10$

$3y-2y=20$

$y=20$

$\Rightarrow x=2(20)+10=40+10=50$

The present ages of A and B are 50 years and 20 years respectively.

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Updated on: 10-Oct-2022

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