Average score of a class of 60 students in an examination is 43. If the average score of the students who have passed is 52 and that of who have failed is 16, then what is the percentage of failed students?
25 %
This is a mixture (alligation) problem. Total students = 60, overall average = 43. Passed students average 52, failed students average 16.
Let the number of failed students = f, so passed = (60 − f).
Total marks the two groups contribute must equal the whole class total:
52(60 − f) + 16f = 43 × 60
Compute: 3120 − 52f + 16f = 2580
3120 − 36f = 2580
36f = 3120 − 2580 = 540
f = 540 / 36 = 15.
Percentage failed = (15 / 60) × 100 = 25 %.
Quick alligation check: distance of overall mean from pass mean = 52 − 43 = 9; from fail mean = 43 − 16 = 27. So passed : failed = 27 : 9 = 3 : 1, meaning failed are 1 part out of 4 = 25 %. The values 28 %, 30 % and 20 % break this exact balance.
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