The following table shows the number of employees of five companies A-E who…
2023
The following table shows the number of employees of five companies A-E who prefer their own vehicle to reach office and percentage (%) of employees who prefer Metro and Bus to reach office. There are only three modes of transport as mentioned. Based on the data in the table, answer the questions that follow.
Company-wise Distribution of Employees Preferring Modes of Transport
Company | Number of Employees who prefer their own Vehicles | Percentage of Employees who prefer Metro | Percentage of Employees who prefer 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 total number of employees who prefer travelling by Metro from A, B and C?
Answer: A. 3908 — ConceptWhen categories exhaust a population, their percentages add to 100%. A count given for one category therefore corresponds to the percentage share left…
- A.
3908
- B.
3710
- C.
3308
- D.
4028
Show answer & explanation
Correct answer: A
Concept
When categories exhaust a population, their percentages add to 100%. A count given for one category therefore corresponds to the percentage share left after subtracting the other category percentages.
The population total is category count divided by that category’s decimal share. Any other category count is then the total multiplied by its decimal percentage.
Application
For company A, the own-vehicle share is 100% − 68% − 24% = 8%. Total employees = 184 ÷ 0.08 = 2300, so Metro employees = 2300 × 0.68 = 1564.
For company B, the own-vehicle share is 100% − 60% − 35% = 5%. Total employees = 78 ÷ 0.05 = 1560, so Metro employees = 1560 × 0.60 = 936.
For company C, the own-vehicle share is 100% − 55% − 30% = 15%. Total employees = 384 ÷ 0.15 = 2560, so Metro employees = 2560 × 0.55 = 1408.
The required Metro total is 1564 + 936 + 1408 = 3908.
Cross-check
The reconstructed counts exhaust each company total: A gives 184 + 1564 + 552 = 2300, B gives 78 + 936 + 546 = 1560, and C gives 384 + 1408 + 768 = 2560.
Result
Therefore, the total number of employees from A, B and C who prefer Metro is 3908.