The following table shows the percentage of students (Boys and Girls) who have…
2022
The following table shows the percentage of students (Boys and Girls) who have successfully completed their respective academic programmes, namely, B.A., B.Sc., B.Com., B.B.A., B.C.A. and B.Tech. in a college. Based on the data in the table, answer the questions 1-5:
Programme-wise Percentage of Successful Students
Programme | Boys | Girls |
|---|---|---|
B.A. | 80% | 60% |
B.Sc. | 80% | 70% |
B.Com. | 40% | 60% |
B.B.A. | 90% | 60% |
B.C.A. | 70% | 80% |
B.Tech. | 70% | 60% |
If the total number of boys and girls in each programme is 150 and 120, respectively, then what is the approximate overall pass percentage of the college?
Answer: B. 69% — ConceptFor several groups, the overall percentage is a weighted percentage: first add the successful counts, then divide by the total enrolment. A simple…
- A.
64%
- B.
69%
- C.
72%
- D.
54%
Attempted by 8 students.
Show answer & explanation
Correct answer: B
Concept
For several groups, the overall percentage is a weighted percentage: first add the successful counts, then divide by the total enrolment.
A simple average of percentages is valid only when the groups have equal sizes; otherwise each rate must be weighted by its group size.
Application
Across six programmes, total boys = 6 × 150 = 900 and total girls = 6 × 120 = 720.
Successful boys = 0.80 × 150 + 0.80 × 150 + 0.40 × 150 + 0.90 × 150 + 0.70 × 150 + 0.70 × 150 = 645.
Successful girls = 0.60 × 120 + 0.70 × 120 + 0.60 × 120 + 0.60 × 120 + 0.80 × 120 + 0.60 × 120 = 468.
Therefore, total successful students = 645 + 468 = 1,113, while total students = 900 + 720 = 1,620.
Overall pass percentage = (1,113 ÷ 1,620) × 100 = 68.70%, approximately 69%.
Cross-check
Boys’ aggregate pass rate = (645 ÷ 900) × 100 = 71.67%.
Girls’ aggregate pass rate = (468 ÷ 720) × 100 = 65%.
Weighting the exact group totals again gives [(645 + 468) ÷ (900 + 720)] × 100 = 68.70%, which rounds to 69% and confirms the result.