Question : The average number of runs scored by a cricketer in 42 innings is 30. The difference between his maximum and minimum scores in an inning is 100. If these two innings are not taken into consideration, then the average score of the remaining 40 innings is 28. What are the maximum runs scored by him in an inning?
Option 1: 120
Option 2: 105
Option 3: 115
Option 4: 110
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Correct Answer: 120
Solution :
Given: The average number of runs scored by a cricketer in 42 innings = 30
If these two innings are not taken into consideration, then the average score of the remaining 40 innings is 28.
Total runs in 40 innings = (40 × 28) = 1120
Total runs in 42 innings = (42 × 30) = 1260
So, the sum of his maximum and minimum scores = (1260 – 1120) = 140
The difference between his maximum and minimum scores in an inning = 100.
Therefore, the maximum score = $\frac{140 + 100}{2}$ = 120
Hence, the correct answer is 120.
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