The average of the ages of three persons A, B, and C is 45 years, and the…
2024
The average of the ages of three persons A, B, and C is 45 years, and the average age of A, C, and D is 51 years. If D is 56 years old, what is the age of B?
Answer: B. 38 years — ConceptFor n quantities, total = average × n. A shared subtotal can be isolated by subtracting the known member from a group total. When two groups contain…
- A.
35 years
- B.
38 years
- C.
36 years
- D.
36.5 years
Show answer & explanation
Correct answer: B
Concept
For n quantities, total = average × n. A shared subtotal can be isolated by subtracting the known member from a group total.
When two groups contain the same shared members, comparing their totals also reveals the difference between the members that were replaced.
Application
The total age of A, B, and C is 45 × 3 = 135 years.
The total age of A, C, and D is 51 × 3 = 153 years.
Since D is 56 years old, A + C = 153 − 56 = 97 years.
Therefore, B = (A + B + C) − (A + C) = 135 − 97 = 38 years.
Cross-check
Replacing B with D raises the average by 51 − 45 = 6 years for three people, so the total rises by 6 × 3 = 18 years.
Thus D − B = 18, giving B = 56 − 18 = 38 years, which agrees with the direct calculation.
Hence, the age of B is 38 years.