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.

Answer 1

So, you know that A is two years older than B, which means that you can write

A=B+2 (1)

You also know that A's father, F, is twice as old as A

F=2⋅A (2)

The same can be said for B and his sister S

B=2⋅S (3)

FInally, you know that the difference between the ge of the father nad the age of the sister is 40 years old, so you can write

F−S=40 (4)

Now you can replace F from equation (2) into equation (4) and B from equation (3) into equation (1) to write

{A=2S+22A−S=40

Replace the value of A from the first equation into the second one to get

2⋅(2S+2)−S=40

4S−S+4=40

3S=36⇒S=363=12

This means that the age of A is

A=2⋅S+2

A=2⋅12+2=26

Answer 2

take s=x years
then b=2x
a= 2 + 2x
f=2(2+2x)

given 2(2+2x)-x=40
4+4x-x=40
3x=36
x=12

A=2+2x=2+2(12)=26yrs