A's age six years ago was equal to twice of B's age four years ago. C is nine years elder to B and also nine years younger to A. What is the sum of present ages of A, B, and C?

A's age six years ago was equal to twice of B's age four years ago. C is nine years elder to B and also nine years younger to A. What is the sum of present ages of A, B, and C? Correct Answer 87 years 

GIVEN:

A's age six years ago was equal to twice of B's age four years ago.

C is nine years elder to B and also nine years younger to A.

CONCEPT:

Basic concept of ages.

CALCULATION:

Suppose present ages of A, B and C are a, b and c respectively.

(a - 6) = 2 × (b - 4)

⇒ 2b - a = 2      ---(i)

Also,

c = b + 9 = a - 9

⇒ a - b = 18      ---(ii)

From equations (i) and (ii):

⇒ b = 20 years and a = 38 years

c = b + 9 = 29 years

∴ Sum of present ages of A, B and C = 38 + 20 + 29 = 87 years

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