The following table shows the number of employees working in five different…
2023
The following table shows the number of employees working in five different companies A-E in December 2021, along with the percentage distribution of Science, Commerce and Arts graduates among them. Use the data to answer the question.
Company-wise Details of Employees
Company | Number of Employees | Science | Commerce | Arts |
|---|---|---|---|---|
A | 2100 | 32% | - | - |
B | 1400 | - | 31% | 40% |
C | - | 30% | 30% | - |
D | - | - | 40% | 20% |
E | - | 35% | 50% | - |
Employees of all five companies are categorised only as Science, Commerce or Arts graduates.
Some values are missing in the table and shown as “-”; calculate them if required.
In Company B, what is the difference between the number of Arts graduates and Science graduates?
Answer: C. 154 — ConceptWhen a whole is divided into exhaustive categories, their percentages total 100%. A category count equals (percentage/100) × total, and the difference…
- A.
174
- B.
178
- C.
154
- D.
146
Show answer & explanation
Correct answer: C
Concept
When a whole is divided into exhaustive categories, their percentages total 100%. A category count equals (percentage/100) × total, and the difference between two category counts equals (percentage-point gap/100) × the same total.
Application
For Company B, let the Science percentage be s%. The three graduate categories are exhaustive, so s + 31 + 40 = 100.
Therefore, s = 100 - 31 - 40 = 29. The Science share is 29%, while the Arts share is 40%.
The percentage-point gap is 40 - 29 = 11.
The required difference in employee counts is 11% of 1,400 = (11/100) × 1,400 = 154.
Cross-check
Arts graduates = 40% of 1,400 = 560, and Science graduates = 29% of 1,400 = 406. Their difference is 560 - 406 = 154, confirming the result.
Result
The difference is 154 employees.