The following table presents data about academic performance of students…
2022
The following table presents data about academic performance of students showing pass percentage (%) and ratio of male to female among passed and failed students of six different colleges A-F in a city. Based on the data in the table, answer the following questions:
College | Pass percentage | Ratio of Male to Female in pass students | Ratio of Male to Female in fail students |
|---|---|---|---|
A | 40% | 12:13 | 12:5 |
B | 55% | 5:3 | 11:14 |
C | 70% | 7:5 | 5:3 |
D | 45% | 4:1 | 7:3 |
E | 50% | 2:1 | 1:2 |
F | 37.50% | 3:2 | 2:1 |
If the number of students who have passed from B and C are equal, then what is the ratio between the number of failed students from B and C, respectively?
Answer: D. 21:11 — ConceptA pass percentage p converts a common passed count P into a total of P/(p/100). The failed count is total minus P, equivalently P(100-p)/p. When two…
- A.
13:23
- B.
23:13
- C.
11:21
- D.
21:11
Show answer & explanation
Correct answer: D
Concept
A pass percentage p converts a common passed count P into a total of P/(p/100). The failed count is total minus P, equivalently P(100-p)/p. When two colleges have the same passed count, P cancels from their failed-count ratio.
Application
Let the equal number of passed students in colleges B and C be P.
For college B, the pass percentage is 55%, so the failed-to-passed ratio is 45:55 = 9:11. Therefore, failed students in B = 9P/11.
For college C, the pass percentage is 70%, so the failed-to-passed ratio is 30:70 = 3:7. Therefore, failed students in C = 3P/7.
Hence, failed students in B : failed students in C = (9P/11) : (3P/7) = 63 : 33 = 21 : 11.
Cross-check
Take P = 385. Then B has 700 total students and 315 failed students, while C has 550 total students and 165 failed students. Thus 315:165 simplifies to 21:11, confirming the result.