The average age of A and B is 25 years. If A is replaced by C, the average becomes 22 years. The average age of C and A is 19 years. What are the ages of A, B and C respectively (in years)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 22, 28, 16
Each average of two gives the sum of that pair. Adding the three pair sums counts every person twice, which gives the total of all three.
A \(+\) B \(=2\times25=50\)
B \(+\) C \(=2\times22=44\)
C \(+\) A \(=2\times19=38\)
A \(+\) B \(+\) C \(\displaystyle =\frac{50+44+38}{2}=66\)
A \(=66-44=22\), B \(=66-38=28\), C \(=66-50=16\)