If the percentage of male employees in office C is 20% and that of female…
2022
If the percentage of male employees in office C is 20% and that of female employees in office D is 40%, then what is the ratio of the number of female employees in office D to that of female employees in office C?
Answer: D. 5:6 — Concept: In a pie chart the central angle of each sector is proportional to the quantity it represents out of 360°. So the total employees in an office are…
- A.
2:3
- B.
3:8
- C.
3:2
- D.
5:6
Show answer & explanation
Correct answer: D
Concept: In a pie chart the central angle of each sector is proportional to the quantity it represents out of 360°. So the total employees in an office are proportional to that office's degree value, and the number of one gender in an office = (that gender's %) × (the office's degree share). A ratio taken between two offices is scale-invariant: the actual grand total cancels, so we may work directly with the degrees.
Application:
Read the two sectors from the chart: office D = 90° and office C = 54°.
Female share of office D = 40% (given). Female employees in D ∝ 0.40 × 90 = 36 units.
Male share of office C = 20%, so female share of C = 100% − 20% = 80%. Female employees in C ∝ 0.80 × 54 = 43.2 units.
Ratio (female in D) : (female in C) = 36 : 43.2 = 360 : 432 = 5 : 6 (dividing both terms by 72).
Cross-check: Put in any concrete total, say 3600 employees. Office D = 3600 × 90/360 = 900, of which 40% are female = 360. Office C = 3600 × 54/360 = 540, of which 80% are female = 432. Then 360 : 432 = 5 : 6 — the same result, which also shows the answer does not depend on the chosen total.
Result: the required ratio is 5 : 6.