In a cricket match, the average runs scored by 7 players is 53. The runs scored by 6 of the players are 121, 40, 26, 56, 37 and 48. How many runs did the seventh player score?

Introduction / Context:
This question is a straightforward application of the definition of average. You know the average runs of all 7 players and the individual scores of 6 of them. To find the missing seventh score, you reconstruct the total runs from the average and subtract the known scores. This type of question reinforces the idea that average carries complete information about the total when the count is known.

Given Data / Assumptions:

• Number of players = 7.
• Average runs of all players = 53.
• Runs of 6 players: 121, 40, 26, 56, 37 and 48.
• Score of the seventh player is unknown.

Concept / Approach:
Average = total runs / number of players. Therefore total runs = average * number of players. Once total runs are known, we subtract the sum of the 6 known scores to get the missing score of the seventh player.

Step-by-Step Solution:
Step 1: Total runs scored by all 7 players = 53 * 7 = 371.Step 2: Sum of known 6 scores = 121 + 40 + 26 + 56 + 37 + 48.Step 3: Compute the sum: 121 + 40 = 161, 161 + 26 = 187, 187 + 56 = 243, 243 + 37 = 280, 280 + 48 = 328.Step 4: Runs scored by the seventh player = 371 − 328 = 43.

Verification / Alternative check:
We can verify by recomputing the average. New list of scores includes 43 as the seventh value. Total runs = 328 + 43 = 371. Average = 371 / 7 = 53, which matches the original average. Therefore, the calculation is correct.

Why Other Options Are Wrong:
Options 26, 37, 48 or 53 would produce totals that do not give an average of 53 when combined with the other six scores. They either overshoot or undershoot the required total of 371 runs, so the average would be different from the stated value.

Common Pitfalls:

• Miscalculating the sum of the known scores.
• Using division incorrectly instead of reconstructing the total from the average.
• Guessing the missing score from the pattern of existing numbers rather than using the formula.

Final Answer:
The seventh player scored 43 runs.