In a class the ratio of female students to the male students is 16:9. What…
2022
In a class the ratio of female students to the male students is 16:9. What percentage of the class is female?
Answer: D. 64% — ConceptWhen two groups are in the ratio a:b, the total number of equal parts is a + b. The percentage represented by the first group is (a / (a + b)) × 100.…
- A.
60%
- B.
55%
- C.
36%
- D.
64%
Attempted by 5 students.
Show answer & explanation
Correct answer: D
Concept
When two groups are in the ratio a:b, the total number of equal parts is a + b.
The percentage represented by the first group is (a / (a + b)) × 100.
Application
Let each ratio part represent k students. Then female students = 16k and male students = 9k.
Total students = 16k + 9k = 25k.
Female fraction of the class = 16k / 25k = 16/25.
Female percentage = (16/25) × 100 = 64%.
Cross-check
If 64% of the class is female, the remaining 36% is male. Thus female:male = 64:36 = 16:9, which reproduces the given ratio.
Therefore, female students form 64% of the class.