In a college, 63% of the number of students are girls and the rest are boys.…
2020
In a college, 63% of the number of students are girls and the rest are boys. If 15% of the number of girls failed and 65% of the number of boys passed in the examination, then the percentage of total number of students who passed is:
- A.
80.2
- B.
67.8
- C.
72.4
- D.
77.6
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept: When a population splits into two groups with different pass rates, the overall pass percentage is the weighted average of each group's own pass rate, weighted by that group's share of the total population — not a plain average of the two given rates.
Application: Take the total number of students as 100 (only the percentages matter, so any total works).
Girls are 63% of the class, i.e. 63 students; boys are the remaining 37%, i.e. 37 students.
15% of the girls failed, so 100% − 15% = 85% of the girls passed: girls who passed = 85% of 63 = 53.55.
65% of the boys passed directly, so boys who passed = 65% of 37 = 24.05.
Total students who passed = 53.55 + 24.05 = 77.6, out of 100 students in all — so 77.6% of the total students passed.
Cross-check: Working from the failures instead: girls who failed = 15% of 63 = 9.45; boys who failed = 35% of 37 = 12.95; total who failed = 22.4. So total who passed = 100 − 22.4 = 77.6%, matching the value obtained above.