# The average weight of all players in the playground initially is 72 kg. If 8 players in the playground having an average weight of 70 kg leave and 2 p

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The average weight of all players in the playground initially is 72 kg. If 8 players in the playground having an average weight of 70 kg leave and 2 players having an average weight of 108 kg join, the average weight of the players in the playground becomes 74 kg. If n players are left which of the following is/are correct?

A. n = 50

B. n + 11 is a multiple of 11

C. n/11 is divided by 4

D. n + 5 is a perfect square

1. Only A
2. C and D
3. B and D
4. B, C and D

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Correct Answer - Option 4 : B, C and D

Given:

Average weight of n players = 72 kg

Average weight of 8 players who leave = 70 kg

Average weight of 2 players who join = 108 kg

Average weight, initially= 74 kg

Formula Used:

Average = Sum of values/Number of values

Calculation:

Sum of weight of 8 players who leave/8 = 70 kg

⇒ Sum of weight of 8 players who leave = 560 kg

Sum of weight of 2 players who join/2 = 108 kg

⇒ Sum of weight of 2 players who join = 216 kg

∵ 8 players leave and 2 join

∴ Number of players initially = n + 6

Sum of weight of n + 6 players/(n + 6) = 72

⇒ Sum of weight of n + 6 players = 72(n + 6)

Sum of weight of n players/n = 74

⇒ Sum of weight of n players = 74n

⇒ 72(n + 6) – 560 + 216 = 74n

⇒ 72n + 432 – 344 = 74n

⇒ 2n = 88

n = 44

A. n = 50

n = 44

⇒ A is not correct

B. n + 11 is a multiple of 11

44 + 11 = 55

⇒ 5 × 11

⇒ B is correct

C. n/11 is divided by 4

44/11 = 4

⇒ C is correct

D. n + 5 is a perfect square

44 + 5 = 49

⇒ 72

⇒ D is correct

B, C, and D are correct