In a match, average of runs scored by five players Is 49. If the runs scored by four players are 75, 30, 62 and 21 respectively, then how many runs did the fifth player score?

Options

A. 43
B. 49
C. 57
D. 89

Answer

To find out how many runs the fifth player scored, we can follow these steps:

### Step 1: Calculate the total runs scored by all five players.
The average runs scored by the five players is given as 49. To find the total runs scored by all five players, we can use the formula:

\[ \text{Total Runs} = \text{Average} \times \text{Number of Players} \]

Substituting the values:

\[ \text{Total Runs} = 49 \times 5 = 245 \]

### Step 2: Calculate the total runs scored by the four players.
The runs scored by the four players are given as 75, 30, 62, and 21. We need to sum these runs:

\[ \text{Total Runs by 4 Players} = 75 + 30 + 62 + 21 \]

Calculating this step-by-step:

- First, add 75 and 30:
\[ 75 + 30 = 105 \]

- Next, add 62 to the result:
\[ 105 + 62 = 167 \]

- Finally, add 21:
\[ 167 + 21 = 188 \]

So, the total runs scored by the four players is 188.

### Step 3: Calculate the runs scored by the fifth player.
Now that we have the total runs scored by all five players and the total runs scored by the four players, we can find the runs scored by the fifth player by subtracting the total runs of the four players from the total runs of all players:

\[ \text{Runs by Fifth Player} = \text{Total Runs} - \text{Total Runs by 4 Players} \]

Substituting the values:

\[ \text{Runs by Fifth Player} = 245 - 188 = 57 \]

Thus, the fifth player scored **57 runs**.

### Summary of Steps:
1. Calculate total runs for all players using average.
2. Sum the runs of the four players.
3. Subtract the sum of the four players from the total runs to find the fifth player's score.