Average runs of 6 players in a cricket match was 36. If one player made 16 runs, then what is the average runs of remaining players ?

Question

Accepted Answer

To determine the average runs of the remaining players, we start by calculating the total runs scored by all 6 players. The average runs of 6 players is given as 36. Therefore, the total runs scored by all players is:

$$ \text{Total runs} = \text{Average runs} \times \text{Number of players} = 36 \times 6 = 216 $$

One player made 16 runs. To find the total runs scored by the remaining 5 players, we subtract the runs made by this player from the total runs:

$$ \text{Total runs by remaining players} = 216 - 16 = 200 $$

Now, we calculate the average runs of the remaining 5 players:

$$ \text{Average runs of remaining players} = \frac{\text{Total runs by remaining players}}{\text{Number of remaining players}} = \frac{200}{5} = 40 $$

Thus, the average runs of the remaining players is 40, which corresponds to Option 4.

**Explanation for why other options are incorrect:**

1. **Option 1 (24):** If the average runs of the remaining players were 24, the total runs for these 5 players would be $ 24 \times 5 = 120 $. Adding the 16 runs from the one player, the total would be $ 120 + 16 = 136 $, which is incorrect because the total runs should be 216.

2. **Option 2 (30):** If the average runs of the remaining players were 30, the total runs for these 5 players would be $ 30 \times 5 = 150 $. Adding the 16 runs from the one player, the total would be $ 150 + 16 = 166 $, which is incorrect because the total runs should be 216.

3. **Option 3 (36):** If the average runs of the remaining players were 36, the total runs for these 5 players would be $ 36 \times 5 = 180 $. Adding the 16 runs from the one player, the total would be $ 180 + 16 = 196 $, which is incorrect because the total runs should be 216.

Therefore, Option 4 is the only correct answer, as it accurately reflects the average runs of the remaining players.