What is the ratio of the total number of graduate female employees of city A…
2024
What is the ratio of the total number of graduate female employees of city A to the total number of non-graduate female employees from city D?
Answer: A. 7:6 — Concept: In a percentage-distribution table a count is never read off directly — it is rebuilt by chained multiplication, part = whole × (that group's share…
- A.
7:6
- B.
8:7
- C.
6:5
- D.
5:4
Show answer & explanation
Correct answer: A
Concept: In a percentage-distribution table a count is never read off directly — it is rebuilt by chained multiplication, part = whole × (that group's share of the whole) × (the percentage that applies within that group). A “non-graduate” percentage is never printed in such a table; it is the complement of the graduate percentage, 100% − g%. And when two such chains are compared as a ratio, any base common to both cancels, so only the chain of percentages decides the ratio.
Application — rebuild the two counts the question asks for:
The six cities together employ 80,000 people with male : female = 9 : 7, so the female workforce is 80,000 × 7/16 = 35,000. This 35,000 — not 80,000 — is the base of the “Percentage Distribution of Female Employees” column.
City A holds 15% of the female employees, so city A has 0.15 × 35,000 = 5,250 female employees.
42% of city A's female employees are graduates, so graduate female employees in city A = 0.42 × 5,250 = 2,205.
City D holds 10% of the female employees, so city D has 0.10 × 35,000 = 3,500 female employees.
46% of city D's female employees are graduates, so the non-graduates are 100% − 46% = 54%, giving 0.54 × 3,500 = 1,890 non-graduate female employees in city D.
The required ratio is therefore 2,205 : 1,890. Dividing both terms by their common factor 315 gives 7 : 6.
Quantity | City A — graduate females | City D — non-graduate females |
|---|---|---|
Female employees | 15% of 35,000 = 5,250 | 10% of 35,000 = 3,500 |
Percentage applied | 42% (graduates) | 54% (= 100% − 46%) |
Resulting count | 2,205 | 1,890 |
Cross-check, two independent ways:
Because the base 35,000 is common to both chains it cancels, so the ratio can be read straight off the percentages: (15 × 42) : (10 × 54) = 630 : 540 = 7 : 6.
As a decimal, 2,205 ÷ 1,890 = 1.1667, and 7 ÷ 6 = 1.1667 as well.
Which columns are irrelevant here, and why:
The “Percentage Distribution of Employees” column (24% for A, 6% for D) splits the combined male-plus-female workforce of 80,000, not the female workforce, so using it in place of the female-distribution column changes both counts.
The “Percentage of Male Graduates” column (26% for A, 36% for D) applies to male employees only and takes no part in a female-to-female comparison.
Required ratio = 7 : 6.