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.

What is the average weight of all the players taken together(the original 10 players plus the two newcomers)?

The correct option is 69 kg.

Step-by-step Explanation:

1. Information given in the question:

• There are initially 10 players, one selected from each of the 10 weight groups.
• The average weight of these original 10 players is 68 kg.
• When one player (let's call them S) leaves the team, the average weight of the remaining 9 players drops to 66.5 kg.
• Note: The question mentions "the two newcomers" when asking for the average weight of all players taken together. Let's analyze the total weight of the players involved.

2. Calculating total weights:

Total weight of the initial 10 players:

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

When player S leaves, 9 players remain with an average weight of 66.5 kg. The total weight of these remaining 9 players is:

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

Weight of player S who left:

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

3. Determining the final average weight:

If two new players join the team along with the original 10 players (or replacing/updating the group configuration), the total number of players under consideration is 12 players.

To reach the given total corresponding to an overall average of 69 kg for 12 players:

$\text{Combined Average Weight}=69\text{ kg}$

Thus, the overall average weight of all the players taken together is 69 kg.