The table gives, for companies A–E, the number of employees who use their own…
2023
The table gives, for companies A–E, the number of employees who use their own vehicles and the percentages who use the Metro and Bus. These are the only three transport modes.
Company | Employees using own vehicles | Metro (%) | Bus (%) |
|---|---|---|---|
A | 184 | 68% | 24% |
B | 78 | 60% | 35% |
C | 384 | 55% | 30% |
D | 182 | 70% | 16% |
E | 220 | 72.5% | 15% |
What is the ratio of the number of employees from company C who travel by Bus to the number from company D who travel by Bus?
Answer: C. 48:13 — CONCEPTWhen categories exhaust a whole, their percentages add to 100%. Therefore, own-vehicle percentage = 100% − Metro percentage − Bus percentage. If a…
- A.
48:19
- B.
48:23
- C.
48:13
- D.
48:11
Show answer & explanation
Correct answer: C
CONCEPT
When categories exhaust a whole, their percentages add to 100%. Therefore, own-vehicle percentage = 100% − Metro percentage − Bus percentage.
If a known count represents p% of a company, total employees = known count × 100/p. A mode count is then total employees × that mode’s percentage/100.
APPLICATION
For company C, own-vehicle percentage = 100% − 55% − 30% = 15%.
Total employees in C = 384 × 100/15 = 2,560.
Bus users in C = 2,560 × 30/100 = 768.
For company D, own-vehicle percentage = 100% − 70% − 16% = 14%.
Total employees in D = 182 × 100/14 = 1,300.
Bus users in D = 1,300 × 16/100 = 208.
Required ratio = 768:208. Dividing both terms by 16 gives 48:13.
CROSS-CHECK
Cross-multiplication verifies the simplified ratio: 768 × 13 = 9,984 and 208 × 48 = 9,984.
Because the cross-products are equal, 768:208 and 48:13 represent the same ratio.
RESULT
The required ratio is 48:13.