Q3 of 266 Page 4

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.

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)


⇒ 2a – b/2 = 40


⇒ 2a – a/2 – 1 = 40


⇒ 3a/2 = 39


⇒ a = 26


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