The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. His highest score is: Options176175174179
Question
The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. His highest score is: Options176175174179
Solution
The total runs scored by the batsman in 40 innings = 40 * 50 = 2000 runs.
When the highest and the lowest scores are excluded, the total number of innings becomes 38 and the average drops by 2 runs to become 48 runs.
So, the total runs scored in 38 innings = 38 * 48 = 1824 runs.
Therefore, the sum of the highest and the lowest scores = 2000 - 1824 = 176 runs.
Given that the highest score exceeds the lowest score by 172 runs, let's denote the lowest score as x. Therefore, the highest score is x + 172.
The sum of the highest and the lowest scores is x + (x + 172) = 176.
Solving this equation gives x = 2, which is the lowest score.
Therefore, the highest score is 2 + 172 = 174 runs.
So, the highest score of the batsman is 174 runs.
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