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.

In the average of all the groups together, which group contributes most in overall average?

The correct answer is Cannot be determined.

Step-by-Step Explanation:

1. Calculate the total weight of all 10 players:
We are given that 1 player is selected from each of the 10 weight groups and their average weight is 68 kg.

$\text{Total Weight}=10\times 68=680\text{kg}$

2. Calculate the total weight of the remaining 9 players:
When player S leaves the team, the average weight of the remaining 9 players becomes 66.5 kg.

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

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

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

This places player S in Group 9 (which covers 80 kg – 84 kg).

4. Analyze the contribution of each group:
Each group is represented by a range of weights rather than fixed, exact weights for the individual players selected. While each group's contribution to the overall average depends on the individual weight of the player chosen from that group, we only know the exact weight of player S (81.5 kg in Group 9). The exact weights of the players in the remaining 9 groups are not explicitly fixed or provided individually.

Since the specific weight values for the individual players across all groups cannot be uniquely determined from the given information alone, the exact group that contributes the most to the overall average Cannot be determined.