In an institute, the average score on an IBACIO Scholarship test for 52 aspirants is 51. Excluding the scores of the top 5 performers, the average score of the remaining aspirants drops by 3. None of the first five highest scores is below 60, and each of the top 5 scorers has distinct integral scores. Determine the maximum possible score of the top performer, considering the maximum score is 200.

Solution

ATQ, Let the score of the topper be 'x' Total score of 52 aspirants = 52 × 51 = 2652 Total score of remaining 47 aspirants after scores of the best five performers are removed  = 47 × 48 = 2256 Total score of the top five aspirants = 2652 – 2256 = 396 x + (total score of the next 4 top scores) = 396 x is the maximum when the total score of the next 4 top scorers is minimum. Total score of the next 4 top scorers has a minimum value of 60 + 61 + 62 + 63 = 246  (since all the top 5 scores are distinct) and the least is 60. Therefore, 'x' has a maximum value of 396 – 246 = 150