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The average age of A and B is 20 years. If A is to be replaced by C, the average would be 19 years. The average age of C and A is 21 years. The ages of A, B and C in order (in years) are
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- 18, 22, 20
- 18, 20, 22
- 22, 18, 20
- 22, 20, 18
- 18, 22, 20
Correct Option: C
Given that , The average age of A and B = 20 years
⇒ A + B = 2 × 20 = 40 .....( 1 )
If A is to be replaced by C, the average of C and B = 19 years
⇒ C + B = 2 × 19 = 38 .....( 2 )
The average age of C and A = 21 years
⇒ C + A = 2 × 21 = 42 .....( 3 )
On adding all three equations , 2 (A + B + C) = 40 + 38 + 42 = 120
⇒ A + B + C = 60
∴ A = (A + B + C) – (B + C) = 60 – 38 = 22 years
B = (A + B + C) – (A + C) = 60 – 42 = 18 years
∴ C = (A + B + C) – (A + B) = 60 – 40 = 20 years
