A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and sister differ by 40 years, find the age of A.

Given:

A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. The ages of the father and sister differ by 40 years.

To do:

We have to find the age of A.

Solution:

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

Age of A’s’ father $= 2x$

Age of B’s sister $= \frac{y}{2}$

According to the question,

$x = y + 2$

$y = x - 2$ ….(i)

$2x - \frac{y}{2} = 40$

$\frac{2(2x)-y}{2}=40$

$4x - y = 80$….(ii)

$4x - (x - 2) = 80$    (From (i))

$4x - x + 2 = 80$

$3x = 80 - 2 = 78$

$x=\frac{78}{3}$

$x = 26$

Age of A $= 26$ years

The age of A is 26 years.

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Updated on: 10-Oct-2022

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