Players are selected for Judo based on their body weights from the following 10 weight groups:
1. (48 kg – 52 kg)
2. (52 kg – 56 kg)
3. (56 kg – 60 kg)
4. (60 kg – 64 kg)
5. (64 kg – 68 kg)
6. (68 kg – 72 kg)
7. (72 kg – 76 kg)
8. (76 kg – 80 kg)
9. (80 kg – 84 kg)
10. (84 kg – 88 kg)

The average weight of the players after selecting one player from each group is 68 kg. If one of the players (named S) leaves the team, their average weight comes down to 66.5 kg.

Player S is from the weight group:

The correct option is 9.

Let us solve the problem step-by-step by finding the total weight of the players before and after player S leaves the team.

Step 1: Calculate the total weight of all 10 players.
Initially, 1 player is selected from each of the 10 weight groups, making a total of 10 players.
The average weight of these 10 players is given as 68 kg.

$\text{Total weight of 10 players}=\text{Number of players}\times \text{Average weight}$

$\text{Total weight of 10 players}=10\times 68=680\text{kg}$

Step 2: Calculate the total weight of the remaining 9 players after player S leaves.
When player S leaves, there are 9 players remaining in the team.
The new average weight of the remaining 9 players is given as 66.5 kg.

$\text{Total weight of 9 players}=9\times 66.5=598.5\text{kg}$

Step 3: Determine the weight of player S.
The weight of player S is the difference between the total weight of all 10 players and the total weight of the remaining 9 players.

$\text{Weight of player S}=680-598.5=81.5\text{kg}$

Step 4: Identify the weight group corresponding to player S's weight.
We check which interval contains 81.5 kg among the 10 weight groups provided:
1. (48 kg – 52 kg)
2. (52 kg – 56 kg)
3. (56 kg – 60 kg)
4. (60 kg – 64 kg)
5. (64 kg – 68 kg)
6. (68 kg – 72 kg)
7. (72 kg – 76 kg)
8. (76 kg – 80 kg)
9. (80 kg – 84 kg)
10. (84 kg – 88 kg)

Since 81.5 kg falls between 80 kg and 84 kg, Player S belongs to weight group 9.