A bowler concedes runs in 5 matches at an average of 45 runs per match and in another 4 matches at an average of 15.75 runs per match. What is the average runs conceded by the bowler over all 9 matches?

Introduction / Context:
This question tests the skill of combining averages from two different blocks of matches to obtain a single overall average. The bowler has different performance levels in two sets of matches, and we need to find the combined average runs conceded. This is a direct application of weighted averages where the weights are the number of matches in each block.

Given Data / Assumptions:

• First block: 5 matches with average runs conceded = 45 runs per match.
• Second block: 4 matches with average runs conceded = 15.75 runs per match.
• Total matches = 5 + 4 = 9.

Concept / Approach:
To combine averages, convert each block's average into a total by multiplying by the number of matches. Then add these totals to get the overall runs conceded and divide by the total number of matches to get the combined average.

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

Verification / Alternative check:
We can see that the second block has a much lower average, so the overall average must fall between 15.75 and 45. The value 32 lies between these bounds and is closer to 45 because more matches belong to the first block. This rough check supports our detailed calculation.

Why Other Options Are Wrong:
Option 15 is too low and close to the second block average, ignoring the heavier weight of the first set of matches. Option 35 is higher than the computed 32 and would require more runs conceded in the lower average block. Option 53.5 is even higher than the first block average, which is impossible. Option 28 is lower than the calculated value and inconsistent with the weighted contributions.

Common Pitfalls:

• Taking a simple average of 45 and 15.75 without weighting by the different numbers of matches.
• Mistakes while multiplying 15.75 by 4 or when adding totals.
• Dividing by 2 instead of 9 after adding the two block totals.

Final Answer:
The average runs conceded by the bowler over all 9 matches is 32 runs per match.