Allan's age is 2 times his son's age. Ten years ago he was four times his son's age. Find their present ages.

To do: Find the present age of Allan and his son.

Solution:

Let son's present age be $y$. 

Then Allan's present age is $2y$

10 years ago, son's age = $y - 10$

Allan's age = $2y - 10$

Given Allan's age four times son's age 10 years ago

or $2y - 10 = 4(y - 10)$ 

 $\Rightarrow2y - 10 = 4y - 40$

$\Rightarrow 4y - 2y = 2y = 40 - 10$

= 30

Solving $y = \frac{30}{2} = 15$

So, son's present age = 15 years and Allan's present age = $2\times15 = 30$yr 

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Updated on: 10-Oct-2022

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