The batting average for 50 innings of a cricket player is 60 runs. His highest score exceeds his lowest score by 180 runs. If these two innings are excluded, the average of the remaining 48 innings is 58 runs. Find the highest score of the player.
Question
The batting average for 50 innings of a cricket player is 60 runs. His highest score exceeds his lowest score by 180 runs. If these two innings are excluded, the average of the remaining 48 innings is 58 runs. Find the highest score of the player.
Solution
Step 1: Calculate the total runs scored in 50 innings.
The average runs scored in 50 innings is 60. Therefore, the total runs scored in 50 innings is 50 * 60 = 3000 runs.
Step 2: Calculate the total runs scored in 48 innings.
The average runs scored in 48 innings is 58. Therefore, the total runs scored in 48 innings is 48 * 58 = 2784 runs.
Step 3: Calculate the total runs scored in the two excluded innings.
The total runs scored in the two excluded innings is the total runs scored in 50 innings minus the total runs scored in 48 innings. Therefore, the total runs scored in the two excluded innings is 3000 - 2784 = 216 runs.
Step 4: Calculate the highest and lowest scores.
We know that the highest score exceeds the lowest score by 180 runs. Let's denote the lowest score as x. Therefore, the highest score is x + 180. The sum of the highest and lowest scores is x + (x + 180) = 216. Solving this equation for x gives x = 18. Therefore, the highest score is 18 + 180 = 198 runs.
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