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% |
In B.Com. programme, 44% of the total students passed. If total number of boys in B.Com. is 200, then what is the total number of girls in B.Com.?
Answer: A. 50 — ConceptWhen subgroups have different success rates, the overall success rate is a weighted average: total successful students divided by total students.…
- A.
50
- B.
52
- C.
66
- D.
60
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
When subgroups have different success rates, the overall success rate is a weighted average: total successful students divided by total students.
Convert each percentage into a successful-student count, add the counts, and equate that total to the stated overall percentage.
Application
Let G be the total number of girls in B.Com. The boys who passed are 40% of 200 = 80.
The girls who passed are 60% of G = 0.60G, so the total who passed is 80 + 0.60G.
Since 44% of all 200 + G students passed, 80 + 0.60G = 0.44(200 + G).
Expanding gives 80 + 0.60G = 88 + 0.44G, so 0.16G = 8.
Therefore, G = 8 ÷ 0.16 = 50.
Cross-check
For 50 girls, 80 boys and 30 girls pass, so 110 of 250 students pass. Since 110 ÷ 250 = 44%, the total number of girls is 50.