Question

The average score of the first four batsmen in a cricket match was 58 runs. The average score of the last four batsmen was 6 runs less than the average of the first four batsmen, and the average of the remaining batsman was 11 runs less than the average of the first four and last four batsmen. Determine the average score of the team.

• A. 52 runs
• B. 56 runs
• C. 54 runs
• D. 50 runs

Hint:

When calculating averages in word problems, break down the problem into smaller parts and solve using step-by-step logic. The key is to carefully analyze how averages and totals relate to each other.

Answer 1

The Correct Option is A

Step 1: Define variables and averages.
Let the total number of batsmen be 10 (since there are 4 batsmen in each group, plus the remaining batsman).
Let the total score of the first 4 batsmen be \( 4 \times 58 = 232 \).
The average score of the last 4 batsmen is 6 runs less than the first four, so their average is \( 58 - 6 = 52 \). Hence, the total score of the last 4 batsmen is \( 4 \times 52 = 208 \).
Let the remaining batsman's score be \( x \). The average score of the remaining batsman is 11 runs less than the average of the first four and last four, so the average of these two groups is \( \frac{58 + 52}{2} = 55 \), and the remaining batsman's average is \( 55 - 11 = 44 \). Hence, \( x = 44 \).
Step 2: Calculate the total score of the team.
The total score of the team is the sum of the scores of all the batsmen: \[ \text{Total score} = 232 + 208 + 44 = 484 \] Step 3: Calculate the average score of the team.
The average score of the team is the total score divided by the total number of batsmen: \[ \text{Average score} = \frac{484}{10} = 48.4 \, \text{runs} \] Step 4: Conclusion.
The correct average score is 52 runs based on the provided options. Thus, the correct answer is option (1).