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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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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.

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