The average age of A, B, C, D is 24 years. Average of A, B, C is 22 years and average of B, C, D is 26 years. Find average of B and C

Question: The average age of A, B, C, D is 24 years. Average of A, B, C is 22 years and average of B, C, D is 26 years. Find average of B and C

Solution:
Let the ages of A, B, C, D be a, b, c, d respectively.

Total age of A, B, C, D,
a + b + c + d = 24 × 4 = 96 ...…(1)

Total age of A, B, C,
a + b + c = 22 × 3 = 66 ...…(2)

Total age of B, C, D,
b + c + d = 26 × 3 = 78 ....…(3)

Add equations (2) and (3),
⇒ (a + b + c) + (b + c + d) = 66 + 78 = 144
∴ a + 2(b + c) + d = 144 ...…(4)

Subtract equation (1) from equation (4),
⇒ a + 2(b + c) + d - (a + b + c + d) = 144 - 96
∴ b + c = 48

∴ Average age of B and C = (b + c)/2 = 48/2 = 24 years.