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. Based on the data in the table, answer the questions that follow.
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% | - |
Note: (1) Employees of all the five companies can be categorised only in three types of Graduates, namely, Science, Commerce and Arts.
(2) Some values are missing in the table (indicated by '-') that you are expected to calculate if required.
In Company E, if the average number of employees who are Graduates in Arts and Commerce is 377, then the number of employees in Company E is
Answer: B. 1160 — ConceptWhen categories are mutually exclusive and exhaustive, their percentages add to 100%. The average of two category counts is their sum divided by 2.…
- A.
1120
- B.
1160
- C.
1320
- D.
1360
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
When categories are mutually exclusive and exhaustive, their percentages add to 100%. The average of two category counts is their sum divided by 2.
Application
Let the total number of employees in Company E be N.
Science is 35% and Commerce is 50%, so Arts = 100% - 35% - 50% = 15%.
Arts employees = 0.15N and Commerce employees = 0.50N.
(0.15N + 0.50N) / 2 = 377.
0.65N = 754, so N = 754 / 0.65 = 1160.
Cross-check
For N = 1160, Arts employees are 174 and Commerce employees are 580. Their average is (174 + 580) / 2 = 377, which matches the given value. Therefore, Company E has 1160 employees.