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A is two years older than B. A’s father D is twice as old as A and B is twice old as his sister C. The ages of D and C differ by 40 years. Find the ages of

Let the age of A be x years. Let the age of B be y years. Since, A is two years older than B, x = y + 2 x - 2 = y........... - (1) A's father D is twice as old as A, So, Age of D = 2 x years. B is twice as old as his sister C. So, Age of C = 1/2 of age of B, i.e. 1/2y years. It is also given that, the ages of D and C differ by 40 years. ⇒ 2x - y/2 = 40 ⇒ 4x - y = 80 ...... - (2) From (1) we have x - 2 = y. So, 4x - (x - 2) = 80 4x - x + 2 = 80 ⇒ 3x = 80 - 2 ⇒ 3x = 78 ⇒x = 26. Putting this value in (1) we get, 26 - 2 = y ⇒ y = 24. Therefore age of A is 26 and B is 24.