This question involves calculating the combined average score of a batsman across multiple matches, given the averages for different sets of matches.

Problem Breakdown: Finding Combined Average Runs

We are given the following information:

• The batsman played 23 matches and scored an average of 40 runs per match.
• The batsman played an additional 10 matches and scored an average of 16 runs per match.
• We need to find the average runs scored across all 33 matches (23 + 10).

To find the overall average, we need to calculate the total runs scored in all matches and then divide by the total number of matches.

Calculating Total Runs

First, let's find the total runs scored in each set of matches:

• Total runs in the first 23 matches: The formula for total runs is Average Runs × Number of Matches. So, total runs = $40 \times 23 = 920$ runs.
• Total runs in the next 10 matches: Similarly, total runs = $16 \times 10 = 160$ runs.

Calculating Overall Average

Now, let's combine the runs and matches:

• Total runs in all 33 matches: Add the runs from both sets: $920 + 160 = 1080$ runs.
• Total number of matches: The total number of matches is $23 + 10 = 33$.
• Overall average runs: The average is the total runs divided by the total number of matches. Average = $\frac{\text{Total Runs}}{\text{Total Matches}} = \frac{1080}{33}$

Final Calculation and Rounding

Performing the division:

$ \frac{1080}{33} \approx 32.727272... $

The question asks to round the average off to two decimal places.

Rounding $32.727272...$ to two decimal places gives $32.73$.

Therefore, the batsman's average runs scored in all 33 matches is approximately 32.73.