The average runs scored by a batsman In 7 matches Is 53 and In other 9 matches the average Is 33. What is the average runs scored by the batsman In 16 matches?

Options

A. 41.75
B. 44.25
C. 47
D. 49.175

Answer

To find the average runs scored by the batsman in 16 matches, we will first calculate the total runs scored in each set of matches and then find the overall average.

### Step 1: Calculate total runs in the first 7 matches
The average runs scored in the first 7 matches is 53.
To find the total runs, we use the formula:
\[ \text{Total Runs} = \text{Average} \times \text{Number of Matches} \]
So, for the first 7 matches:
\[ \text{Total Runs in 7 matches} = 53 \times 7 = 371 \]

### Step 2: Calculate total runs in the next 9 matches
The average runs scored in the next 9 matches is 33.
Using the same formula:
\[ \text{Total Runs in 9 matches} = 33 \times 9 = 297 \]

### Step 3: Calculate total runs in all 16 matches
Now, we will add the total runs from both sets of matches to find the overall total:
\[ \text{Total Runs in 16 matches} = \text{Total Runs in 7 matches} + \text{Total Runs in 9 matches} \]
\[ \text{Total Runs in 16 matches} = 371 + 297 = 668 \]

### Step 4: Calculate the average runs in 16 matches
Finally, we calculate the average runs scored in all 16 matches using the total runs and the total number of matches:
\[ \text{Average} = \frac{\text{Total Runs}}{\text{Total Matches}} = \frac{668}{16} \]
Calculating this gives:
\[ \text{Average} = 41.75 \]

### Final Answer:
The average runs scored by the batsman in 16 matches is **41.75**.

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