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The ratio of present ages of A and B is 3 ∶ 4. 4 years from now the sum of ages of A and C will be 40 years and 6 years from now the sum of ages of B and C will be 50 years. What will be the sum of ages of A, B and C 3 years from now?

The ratio of present ages of A and B is 3 ∶ 4. 4 years from now the sum of ages of A and C will be 40 years and 6 years from now the sum of ages of B and C will be 50 years. What will be the sum of ages of A, B and C 3 years from now? Correct Answer 65

Given:

Present age of A : Present age of B = 3 : 4

After 4 years, Age of (A + C) = 40

After 6 years, Age of (B + C) = 50

Calculation:

Let the present age of A = 3x

Present age of B = 4x

Present age of C = c

According to the question,

(3x + 4) + (c + 4) = 40

⇒ 3x + c = 32     ----(1)

Again, According to the question,

(4x + 6) +(c + 6) = 50

⇒ 4x + c = 38     ----(2)

From (2) – (1), we get

⇒ x = 6

⇒ c = 32 – 3 × 6 = 14

Now, Sum of ages of A, B and C 3 years from now,

(3 × 6 + 3) + (4 × 6 + 3) + (14 + 3)

⇒ 65

∴ The sum of ages of A, B and C 3 years from now is 65.

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