Question

A factory has 500 workers, 15% of whom are women. If 50 additional workers are to be hired and all the present workers remain, how many of the additional workers must be women in order to raise the percentage of women employees to 20%?
A. 3
B. 10
C. 25
D. 30
E. 35

Answer 1

Hint: Out of the total 500 workers, find the number of women working. In the additional 50 workers, find the number of women workers. Consider new workers as ‘w’. So find the total workers as the number of women after hire to the total number of workers.

Complete step by step answer:
Given that the factory has a total of 500 workers.
Out of this 500, 15%of the workers in the factory are women. Now let us find the number of women currently working in the factory.
Number of women = 15% of total workers = 15% of 500 \[=\dfrac{15}{100}\times 500=75\].
\[\therefore \]Number of women workers = 75.
It is said that 50 additional workers are hired and all the present workers remain. We need to find how many of these 50 additional workers should be women in order to raise the percentage of women employees from 15% to 20%.
Thus we can say that,
\[\dfrac{\text{number of women after hire}}{\text{total workers after hire}}=20\%........(1)\]
Let ‘w’ be the number of women hired.
Total workers in the factory after hire = 500 + 50 = 550.
\[\therefore \]Total number of women after hire = 75 +w
\[\therefore \]Thus by giving these values in equation (1), we get,
\[\dfrac{\text {number of women after hire}}{\text{total workers after hire}}=20\%\]
\[\therefore \dfrac{75+w}{550}=\dfrac{20}{100}\]
Cross multiply and simplify the above expression.
\[\begin{align}
  & 75+w=\dfrac{20\times 550}{100} \\
 & 75+w=110 \\
\end{align}\]
\[\therefore w=110-75=35\]
Thus the number of additional women should be 35 out of the 50 new workers, so as to raise the women employment from 15% to 20%.
\[\therefore \]Additional number of women = 35.

Option C is the correct answer.

Note:
We can also use a mixture method to solve the problem.
Let’s say we add (15% of females of 550 people) \[\times \] (% of females in 50 people) = 20%
So we have \[\dfrac{x-20}{5}=\dfrac{500}{50}\]