The average runs scored by a batsman in 23 matches is 41. In the next 10 matches, the batsman scored an average of 16 runs. Find his average runs scored (rounded off to two decimal places) in all the 33 matches.

The correct option is 33.42.

To find the overall average of runs scored by the batsman across all 33 matches, we need to calculate the total runs scored in all the matches combined and then divide by the total number of matches.

Step 1: Calculate total runs scored in the first 23 matches
Given that the average runs scored in 23 matches is 41:
Total runs in 23 matches = Number of matches × Average runs
Total runs in 23 matches = 23 × 41 = 943

Step 2: Calculate total runs scored in the next 10 matches
Given that the average runs scored in the next 10 matches is 16:
Total runs in 10 matches = Number of matches × Average runs
Total runs in 10 matches = 10 × 16 = 160

Step 3: Calculate total runs scored in all 33 matches
Total runs in 33 matches = Total runs in first 23 matches + Total runs in next 10 matches
Total runs in 33 matches = 943 + 160 = 1103

Step 4: Calculate the overall average for all 33 matches
Overall average = Total runs in 33 matches ÷ Total number of matches

$\text{Overall average}=\frac{1103}{33}\approx \mathrm{33.4242...}$

Rounding off to two decimal places gives 33.42.