If the ratio of the number of male and female employees in the Accounts…
2024
If the ratio of the number of male and female employees in the Accounts department is 5 : 4 and 60% of the employees in the HR department are female, what is the total number of male employees in the Accounts and HR departments together?
Answer: A. 592 — ConceptIf a category is p% of a total N, then its count is (p/100) × N; equivalently, N = category count ÷ (p/100). For a ratio a : b, the first group is a/(a…
- A.
592
- B.
594
- C.
596
- D.
598
Attempted by 13 students.
Show answer & explanation
Correct answer: A
Concept
If a category is p% of a total N, then its count is (p/100) × N; equivalently, N = category count ÷ (p/100).
For a ratio a : b, the first group is a/(a + b) of the combined group. A stated percentage can likewise be converted to its complementary percentage.
Application
Marketing is 14% of the company and has 560 employees, so the total number of employees is 560 ÷ 0.14 = 4000.
Accounts has 18% of 4000 employees: 0.18 × 4000 = 720.
The male-to-female ratio in Accounts is 5 : 4, so the male share is 5/(5 + 4) = 5/9. Thus, male employees in Accounts = (5/9) × 720 = 400.
HR has 12% of 4000 employees: 0.12 × 4000 = 480.
If 60% of HR employees are female, then 40% are male. Thus, male employees in HR = 0.40 × 480 = 192.
Therefore, the total number of male employees in Accounts and HR together is 400 + 192 = 592.
Cross-check
The department percentages sum to 100%, and 14% of the recovered total 4000 equals the given Marketing count 560. Also, the Accounts split 400 : 320 simplifies to 5 : 4, confirming the ratio calculation.