The average age of a family of 4 members, 4 years back, was 19 years. A new…

Concept

For any group, Sum of ages = Average age × Number of members. When time passes, every existing member ages by that many years, so the group's total age increases by (years elapsed × number of existing members). When a new member joins, the new average is the new total age divided by the new number of members.

Application

1. 4 years back, the average age of the 4 family members was 19 years, so their total age then = 19 × 4 = 76 years.

2. 4 years have since passed, so each of these 4 members has aged by 4 years; their total age has increased by 4 × 4 = 16 years. Present total age of the original 4 members = 76 + 16 = 92 years.

3. Let the child's present age be K years. The family now has 5 members (4 original + 1 child).

4. The average age of the family is kept the same as it was 4 years back, i.e. 19 years. So: 19 = (92 + K) / 5

5. Solving: 92 + K = 19 × 5 = 95, so K = 95 - 92 = 3.

6. The child's present age is 3 years.

Cross-check

Total age of all 5 members now = 92 + 3 = 95 years. Average = 95 ÷ 5 = 19 years, which matches the average from 4 years back — confirming the answer.