The batting average of a cricket player for 64 innings is 62 runs. His highest score exceeds his lowest score by 180 runs. Excluding these two innings, the average of remaining innings becomes 60 runs. His highest score was?
Question
The batting average of a cricket player for 64 innings is 62 runs. His highest score exceeds his lowest score by 180 runs. Excluding these two innings, the average of remaining innings becomes 60 runs. His highest score was?
Solution
Sure, let's solve this step by step:
- The total runs scored in 64 innings = 64 * 62 = 3968 runs
- The total runs scored in the remaining 62 innings = 62 * 60 = 3720 runs
- Therefore, the total runs scored in the highest and lowest innings = 3968 - 3720 = 248 runs
- Given that the highest score exceeds the lowest score by 180 runs, let's denote the lowest score as 'x'. Therefore, the highest score will be 'x + 180'.
- So, x + (x + 180) = 248
- Solving this equation gives x = 34
- Therefore, the highest score = x + 180 = 34 + 180 = 214 runs
So, the highest score of the cricket player was 214 runs.
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