The average weight of some persons in a club was 80 kg . Seven persons with average weight 85.2 kg joined the

Question

The average weight of some persons in a club was 80 kg . Seven persons with average weight 85.2 kg joined the club and at the same time 2 persons with average weight 72.7 kg left the club. The average weight of all the persons in the group increased by 1.02 kg . How many people were there initially

Accepted Answer

Let the initial number of people in the club be

n

.
Initial total weight

= 80 n

.

Now, 7 persons with average weight

85.2 kg

join, and 2 persons with average weight

72.7 kg

leave.

Net weight added = (7 \times 85.2) - (2 \times 72.7)

Net weight added = 596.4 - 145.4 = 451 kg

The new number of people in the club

= n + 7 - 2 = n + 5

.
The new average weight increased by

1.02 kg

, becoming

80 + 1.02 = 81.02 kg

.

New Total Weight = Initial Total Weight + Net weight added

(n + 5) \times 81.02 = 80 n + 451

81.02 n + 405.1 = 80 n + 451

81.02 n - 80 n = 451 - 405.1

1.02 n = 45.9

n = \frac{45.9}{1.02} = 45

Thus, there were initially

45

people in the club.

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