The following table shows the percentages of boys and girls who successfully…
2022
The following table shows the percentages of boys and girls who successfully completed B.A., B.Sc., B.Com., B.B.A., B.C.A. and B.Tech. programmes in a college. Use the table to answer the question.
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 ratio of the total number of boys to the total number of girls in the B.C.A. programme is 4 : 1, what is the ratio of the number of boys who successfully completed B.C.A. to the number of girls who successfully completed B.C.A.?
Answer: D. 7 : 2 — ConceptWhen two groups have a total-number ratio a : b and their success rates are p% and q%, the successful-number ratio is (p/100 × a) : (q/100 × b). The…
- A.
9 : 4
- B.
9 : 5
- C.
6 : 7
- D.
7 : 2
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept
When two groups have a total-number ratio a : b and their success rates are p% and q%, the successful-number ratio is (p/100 × a) : (q/100 × b). The same scale factor may be used for both original group sizes because it cancels from the final ratio.
Application
Let the total numbers of B.C.A. boys and girls be 4x and x, respectively.
Successful boys = 70% of 4x = (70/100) × 4x = 2.8x.
Successful girls = 80% of x = (80/100) × x = 0.8x.
Therefore, the required ratio = 2.8x : 0.8x = 28 : 8 = 7 : 2.
Cross-check
Take 400 boys and 100 girls, which preserves the 4 : 1 enrolment ratio. Then 70% of 400 is 280 and 80% of 100 is 80; 280 : 80 simplifies to 7 : 2.