Question

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.

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Solution

Let the present ages of A, B, F and S be x, y, z and t years respectively.

A is elder to B by 2 years. Thus, we have

F is twice as old as A. Thus, we have

B is twice as old as S. Thus, we have

The ages of F and S is differing by 40 years. Thus, we have

So, we have four equations

……(1)

……(2)

……(3)

……(4)

Here x, y, z and t are unknowns. We have to find the value of x.

By using the third equation, the first equation becomes

From the fourth equation, we have

Hence, we have

Using the second equation, we have

Hence, the age of A isyears.

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