Question

A batsman has an average of 53 runs in his 13 innings. The difference between his maximum and minimum score is 114. If these two innings are removed, his average for 11 innings comes down to 45. What is his maximum score?

(a) 85
(b) 90
(c) 95
(d) 100

Answer 1

To find the maximum score of the batsman, we calculate the sum of his scores in all 13 innings, subtract the sum of his scores in the 11 innings after removing two innings, and then subtract the minimum score from the difference to find the maximum score.

Step-by-step explanation:

To find the maximum score of the batsman, we need to first calculate the sum of his scores in all 13 innings by multiplying his average by the number of innings played. The sum comes out to be 53 x 13 = 689.

Next, we subtract the sum of the scores in the 11 innings after removing the two innings from the total sum. The sum of the scores in the 11 innings is 45 x 11 = 495. The difference between the two sums represents the sum of the scores in the two removed innings, which is 689 - 495 = 194.

Since we know that the difference between the maximum and minimum scores is 114, and the sum of the scores in the two removed innings is 194, we can determine the maximum score by subtracting the minimum score (114) from the sum of the scores in the two removed innings (194). Therefore, the maximum score is 194 - 114 = 80.