The average age of a group of workers is 42 yrs. If eight (8) new workers of…

Concept: The average of a group is its total value divided by the number of members, so total = average × count. When two groups are merged, their totals add and their counts add, and the combined average is (sum of the totals) ÷ (sum of the counts).

Application: Let n be the number of workers present at the start.

1. The initial group has n workers averaging 42 years, so its total age is 42n years.

2. The 8 workers who join average 36 years, so their total age is 8 × 36 = 288 years.

3. After they join, the group has (n + 8) members and a total age of (42n + 288) years.

4. The merged average is given as 40 years, so 42n + 288 = 40(n + 8), i.e. 42n + 288 = 40n + 320.

5. Collecting like terms: 42n − 40n = 320 − 288, so 2n = 32 and n = 16.

Cross-check: With n = 16, the initial total is 42 × 16 = 672 years; adding 288 years gives 960 years shared by 24 members, and 960 ÷ 24 = 40 years, which matches the merged average stated in the question.

Faster route (deviation method): Each newcomer is 6 years below the old average of 42, so the 8 newcomers remove 8 × 6 = 48 year-units of surplus. That surplus is spread over the whole merged group and pulls the mean down by 42 − 40 = 2 years, so the merged group has 48 ÷ 2 = 24 members, which means 24 − 8 = 16 workers were present initially.