The average weight of some persons in a group was 63.5 kg. When 5 persons with eights of 72 kg, 75.8 kg, 76 kg, 72.2 kg and 65 kg joined the group and 9 persons with an average weight of 68 kg left the group, then the average weight of all the persons in the group increased by 0.05 kg. What was the number of persons in the group, initially?

Given:

The average weight of some persons in a group was 63.5 kg. When 5 persons with eights of 72 kg, 75.8 kg, 76 kg, 72.2 kg and 65 kg joined the group and 9 persons with an average weight of 68 kg left the group, then the average weight of all the persons in the group increased by 0.05 kg. 

Concept used:

Total = Average × Number of entities

Calculation:

Let there be initially N persons in the group.

Total add-on weight = 72 + 75.8 + 76 + 72.2 + 65

⇒ 361 kg

Total weight of 9 people who left the group = 9 × 68

⇒ 612 kg

Number of members remaining in the group = N + 5 - 9

⇒ (N - 4)

According to the question,

(N - 4) × (63.5 + 0.05) = N × 63.5 + 361 - 612

⇒ 63.55N - 254.2 = 63.5N - 251

⇒ 0.05N = 254.2 - 251

⇒ N = 3.2/0.05

⇒ N = 64

∴ There were 64 people in the group initially.