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

⇒ 7^{2}

⇒ D is correct

**∴ ****B, C, and D are correct**