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.

Match the items on the right to the items on the left.

STEP 1

STEP 2

STEP 3

STEP 4

STEP 5

Let the present ages of A, B, F and S be ‘a’, ‘b’, ‘c’ and ‘d’ respectively.

Given, A is elder to B by 2 years

⇒ a = b + 2 -------- (1)

A’s father F is twice as old as A and B is twice as old as his sister S

⇒ c = 2a and b = 2d ------- (2)

Also, the ages of the father and sister differ by 40 years.

⇒ c – d = 40 ------- (3)

From [2], we have
⇒ 2a – b/2 = 40

Hence, Age of 'A' is 26 years.