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 |
Find the ratio of number of male to female students in D?
Answer: A. 149:51 — ConceptWhen a population is split into groups, convert each group ratio into fractional shares, multiply by that group’s share of the total, and then add…
- A.
149:51
- B.
51:149
- C.
3:1
- D.
1:3
Attempted by 5 students.
Show answer & explanation
Correct answer: A
Concept
When a population is split into groups, convert each group ratio into fractional shares, multiply by that group’s share of the total, and then add corresponding shares. A convenient assumed total can remove percentage denominators without changing the final ratio.
Application
Assume College D has 200 students. With a 45% pass rate, 90 pass and 110 fail.
Among the 90 passed students, the male:female ratio 4:1 gives males = 90 × 4/5 = 72 and females = 90 × 1/5 = 18.
Among the 110 failed students, the male:female ratio 7:3 gives males = 110 × 7/10 = 77 and females = 110 × 3/10 = 33.
Therefore, total males = 72 + 77 = 149 and total females = 18 + 33 = 51. Thus the required ratio is 149:51.
Cross-check
The weighted male share is 0.45 × 4/5 + 0.55 × 7/10 = 0.745, so the female share is 0.255. Multiplying 0.745:0.255 by 200 gives 149:51.