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 average number of employees in A, B and D?
Answer: D. 1720 — CONCEPTWhen categories are exhaustive, the unlisted share is the residual: 100% minus the sum of the listed percentages. If p% of a group equals a known count…
- A.
1850
- B.
1750
- C.
1620
- D.
1720
Show answer & explanation
Correct answer: D
CONCEPT
When categories are exhaustive, the unlisted share is the residual: 100% minus the sum of the listed percentages. If p% of a group equals a known count v, then the total group size is v × 100 ÷ p. The arithmetic mean of n values is their sum divided by n.
APPLICATION
For A, the own-vehicle share is 100% − 68% − 24% = 8%, so the total number of employees is 184 × 100 ÷ 8 = 2300.
For B, the own-vehicle share is 100% − 60% − 35% = 5%, so the total number of employees is 78 × 100 ÷ 5 = 1560.
For D, the own-vehicle share is 100% − 70% − 16% = 14%, so the total number of employees is 182 × 100 ÷ 14 = 1300.
Therefore, the required average is (2300 + 1560 + 1300) ÷ 3 = 5160 ÷ 3 = 1720 employees.
CROSS-CHECK
The residual shares reproduce the given own-vehicle counts: 8% of 2300 is 184, 5% of 1560 is 78, and 14% of 1300 is 182. Their total is 5160, and 5160 ÷ 3 is 1720.