Question
The average score of a group of 50 students is 90. When
the scores of 4 students—X, Y, Z, and W—are excluded, the average of the rest falls by 2. If X scored 10 more than Y, Y scored 25 more than Z, and Z scored 20 less than W, then how much did X score?Solution
ATQ,
Total score of all 50 students = 50 × 90 = 4500 Total score of remaining 46 students = 46 × 88 = 4048 Score of X, Y, Z, W combined = 4500 – 4048 = 452 Let score of X = x Then, Y = x – 10 Z = x – 10 – 25 = x – 35 W = x – 35 + 20 = x – 15 Sum = x + (x – 10) + (x – 35) + (x – 15) = 4x – 60 = 452 → 4x = 452 + 60 = 512 → x = 512 ÷ 4 = 128
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