The average age of three person A, B and C after 17 years will be

SOLUTION

Let current age of A, B and C be a, b and c

Given

(a + 17 + b + 17 + c + 17)/3 = a + b

And (c + 17) = 2b

Calculation

a + 17 + b + 17 + c + 17)/3 = a + b

⇒ a + b + c + 51 = 3a + 3b

⇒ 2a + 2b – c = 51      ----(i)

And we have c + 17 = 2b

⇒ c = 2b - 17     ----(ii)

Putting (i) in (ii)

2a + 2b – 2b + 17 = 51

⇒2a = 34

⇒ a = 17

According to question, difference of age of A and B after 25 years is will be 2 so current difference of ages of A and B is also 2

⇒ a – b = 2       ----(iii)   or   b – a = 2      ----(iv)

From equation (iii) if a = 17 then b = 15 and c = 2b – 17 = 30 – 17 = 13