A factory has 500 workers

We could take an algebraic approach, try out numbers from the answer choices, or just think through logically.

Logically: there will be 550 workers. We'll want 20% of them (or 110) to be women. There are currently 15%*500 = 75 women. The additional number of women must therefore be 110-75 = 35. The full solution below is taken from the GMATFix App.



-Patrick

BlueDragon2010 wrote:A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?

Presently -

Women - 75

Men - 425

The factory is planning Increase in Workforce to the existing strength by 50 Persons , hence total Population will be 550 Persons.

Women will be 20% or 1/5th of 550 = 110 Women

Men Will be 440


So , additional women to be hired will be 110 - 75 = 35 additional women workers.

BlueDragon2010 wrote:A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?

A) 3

B) 10

C) 25

D) 30

E) 35

Solution:

Let's first determine the number of women currently working at the factory. We know that there are 500 workers, and 15% of them are women. Thus, we know there are:

500 x 0.15 = 75 women

We are asked, if 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent? To translate this idea into a mathematical statement, we have:

(Number of women after hire)/(total workers after hire) = 20%

To solve this statement, we can set up the actual equation with the numbers given from the question stem, and we can let w be the number of additional women hired:

(75 + w)/(500 + 50) = 20%

(75 + w)/550 = 0.2

75 + w = 550 x 0.2

75 + w = 110

w = 35

Answer:E