# A is Elder to B by 2 Years

## 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 age of the father and sister differ by 40 years, find the age of A.

We can solve such problems using methods to solve linear equations.

## Answer: The age of A is 26 years.

There are several comparisons given in the question. Using them, we can form some linear equations.

## Explanation:

Suppose the age of A is x, the age of B is y, the age of A's father is z and the age of B's sister is w.

A is elder to B by 2 years. Therefore, we can write it as x = y + 2

A's father is twice as old as A. Therefore, we can write it as z = 2 × x

B is twice as old as his sister. Therefore, we can write it as y = 2 × w

The age of A's father and B's sister differs by 40 years. Therefore, we can write it as z - w = 40

Now, The final set of linear equations are as follows.

x = y + 2 ------ (1)

z = 2 × x ------ (2)

w = y/2 ------- (3)

z - w = 40 ---- (4)

We can substitute value of z and w from equation (2) and (3) respectively in equation (4).

Therefore the 4th equation becomes 2 × x - y/2 = 40

4 × x - y = 80 ---- ( 5 )

4 × ( y + 2 ) - y = 80 {from equation (1)}

4y + 8 - y = 80

3y = 72

y = 24

Hence, we substitute value of y in equation (1)

Thus, x = 24 + 2 = 26