Question

The average age of a family consisting of parents and a child five years ago was 27 years. Three years ago, the average age of parents was 41. The child was born years_________ ago.

• A. 16
• B. 4
• C. 8
• D. 2

Answer 1

Answer:

C. 8

Let present ages of father, mother, and child be (F, M, C).

From 5 years ago

$\frac{(F-5)+(M-5)+(C-5)}{3} = 27$

$F + M + C - 15 = 81$

$F + M + C = 96 \quad \text{(1)}$

From 3 years ago (parents only)

$\frac{(F-3)+(M-3)}{2} = 41$
$F + M - 6 = 82$
$F + M = 88 \quad \text{(2)}$
Find child’s present age

From (1) and (2):
$C = 96 - 88 = 8$

Find when the child was born

Child’s present age = 8 years
So, the child was born 8 years ago.