A firm has 40 workers working in factory premises, 30 working in its office and 20 working in both places. How many workers are there in the firm? How many are working in the : (1).factory (2). office alone.
Answers
Answer:
90 worked are working in the firm
Step-by-step explanation:
For total no of workers, we have to add the total workers. i.e. 40+30+20=90
(1) 60.
This is because 20 workers are working in both factory premises and office. therefore
Worker in factory+ Workers in both=workers in factory
i.e. 40+20=60
(2) 30.
Given:
In a certain firm, 40 workers were working in a factory premised, 30 were working in the office, and 20 were working in both the places.
To Find:
1. The total number of workers working in the factory.
2. The total number of workers working in the office.
Solution:
The given problem can be solved using the concepts of sets.
1. Let the number of workers working on the factory premises be denoted under the set A,
=> n(A) = 40.
2. Let the number of workers working in the office be denoted under the set B,
=> n(B) = 30.
3. A total of 20 people are working at both places,
=> n(A∩B) = 20.
4. The total number of workers working in the factory is calculated as,
=> Total workers in the factory = n(A) + n(B) - n(A∩B),
=> Total workers in the factory = 40 + 30 - 20,
=> Total workers in the factory = 50.
5. The number of workers working in the office alone is,
=> n(B) - n(A∩B),
=> 30 - 20,
=> 10.
Therefore, the number of workers in the factory is 50 and the number of workers in the office alone is 10.