Averages , Ratio and Proportion Question 5 - CAT 2021
Question
The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is:
Step-by-Step Explanation
- Determine the total sum of scores:
Total score pool = 25 students × 50 = 1250 marks.
Let T represent the score of each of the 5 toppers.
- Apply optimization principles to maximize the toppers' score:
To maximize T, we must minimize the combined scores of the remaining 20 students.
These 20 scores must be distinct integers, with the lowest score bound at 30.
Minimum distinct scores = 30, 31, 32, …, 49
Sum of these 20 scores = (20/2) × (30 + 49) = 10 × 79 = 790
- Isolate the toppers' values:
Remaining sum for toppers = 1250 − 790 = 460
5T = 460
T = 92
Correct Answer: 92