A bowler concedes runs in 9 cricket matches. The average runs conceded in the first 5 matches is 45 and the average runs conceded in the remaining 4 matches is 15.75. What is the average number of runs conceded per match over all 9 matches?

Introduction / Context:
This question is about combining averages from two groups of matches to find a single overall average. The bowler has very different performances in two sets of matches, and we need the combined average runs conceded across all matches.

Given Data / Assumptions:
- Number of matches in first group = 5. - Average runs conceded in first 5 matches = 45. - Number of matches in second group = 4. - Average runs conceded in last 4 matches = 15.75. - Total matches played = 9.

Concept / Approach:
To find the combined average, we first find the total runs conceded in each group using average * number of matches. Adding these totals gives total runs for all 9 matches. Finally we divide this overall total by 9 to get the combined average. This is a typical weighted average situation where more matches weigh more heavily.

Step-by-Step Solution:
Step 1: Total runs in the first 5 matches = 5 * 45 = 225. Step 2: Total runs in the last 4 matches = 4 * 15.75. Step 3: 4 * 15.75 = 63. Step 4: Total runs in all 9 matches = 225 + 63 = 288. Step 5: Total matches = 5 + 4 = 9. Step 6: Combined average runs conceded = 288 / 9 = 32.

Verification / Alternative check:
Note that the average 32 is between 15.75 and 45, closer to 45 because there are more matches in the first group. This behaviour matches how weighted averages work, so the answer is reasonable. Rechecking the arithmetic 225 + 63 = 288 and 288 / 9 = 32 confirms the calculation.

Why Other Options Are Wrong:
- 15 and 35 are either too low or too high compared with the weighted average. - 53.5 is larger than even the first group average of 45, so it cannot be correct. - 28 results from incorrect summation or division.

Common Pitfalls:
A frequent error is to simply average 45 and 15.75 without weighting, which ignores that they cover different numbers of matches. Another mistake is to divide the total runs by 2 instead of 9. Always multiply averages by their counts to recover totals, then compute a new overall average correctly.

Final Answer:
The average runs conceded over 9 matches is 32.