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A factory has 500 workers, 15 percent of whom are women. If

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A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 17 Dec 2012, 06:00
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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
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 17 Dec 2012, 06:04
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Walkabout 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


Currently the factory has 0.15*500=75 women.

After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550=110 of them to be women, so we need 110-75=35 more women.

Answer: E.
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 03 Jul 2013, 09:08
We also can use mixture method

Say we add to 15% females of 550 ppl x % females of 50 ppl to get 20% females
So we have (x-20)/5=500/50
X=70%
70%of 50=35
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 03 Jul 2013, 09:22
1
Or

(75+x)/550=20%
X =35
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 22 Aug 2014, 19:24
I also solved this as a mixture problem (see image attached) where w denotes the number of new women hired.

Once I had the table set up I solved (75+w) / 550 = 0.20 => 75+w = 110 => w=35.

Therefore, 35 of the 50 workers hired need to be women.
Attachments

Mixture.png
Mixture.png [ 2.83 KiB | Viewed 12830 times ]

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A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post Updated on: 30 Oct 2014, 23:34
LalaB wrote:
We also can use mixture method

Say we add to 15% females of 550 ppl x % females of 50 ppl to get 20% females
So we have (x-20)/5=500/50
X=70%
70%of 50=35


Hello, could anyone please explain how we came into that equation from the first line?

I am clear up to this:
15% of 500 + x% of 50 = 20% of 550 [correction: 15% of 500, not 550]

* Then how can I come to the highlighted equation. Am I missing anything?

Originally posted by appleid on 30 Oct 2014, 23:26.
Last edited by appleid on 30 Oct 2014, 23:34, edited 1 time in total.
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 04 Nov 2014, 00:12
appleid wrote:
LalaB wrote:
We also can use mixture method

Say we add to 15% females of 550 ppl x % females of 50 ppl to get 20% females
So we have (x-20)/5=500/50
X=70%
70%of 50=35


Hello, could anyone please explain how we came into that equation from the first line?

I am clear up to this:
15% of 500 + x% of 50 = 20% of 550 [correction: 15% of 500, not 550]

* Then how can I come to the highlighted equation. Am I missing anything?



Its called allegation method:

15% .................. x%

............. 20% ...............

(20-15)% .............. (x-20)%

\(\frac{x-20}{5} = \frac{500}{50}\)

x = 70%

\(\frac{70}{100} * 50 = 35\)

Answer = E
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 19 Jan 2015, 01:14
Or, setting up an equation:

First, find how many women we have: 500*0.15 = 75 women now.
We need the number of women to be 20% of the total number of employees.

We will have 50 new employees, making the total # 500+50=550. We need to know how many of the additional workers need to be women in order for the women to be 0.20(550).

In other words: 75+x=0.20(550). This means how many women should we add to the 75 we already have so that the total # of women is 20% of the total # of workers (550).

Solving the equation we get:
75 + x = 0.20(550)
75 + x = 110
x = 110-75
x = 35 ANS E
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 09 May 2016, 06:35
1
1
Walkabout 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


To solve this problem we first need to determine the number of women. We know that there are 500 people and 15% of them are women. Thus we know:

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 to a mathematical statement we have:

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

To solve this statement, we can set up the actual equation with the numbers given in the question stem, and we 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.
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 27 Dec 2017, 20:23
Bunuel, niks18

Quote:
After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550=110 of them to be women, so we need 110-75=35 more women.


I miscalculated 20% of female workers as 1.2x of 75 since in Q we are given:
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

If earlier no of female workers is 75 then do we not need to perform 1.2*75?
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 29 Dec 2017, 10:25
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adkikani wrote:
Bunuel, niks18

Quote:
After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550=110 of them to be women, so we need 110-75=35 more women.


I miscalculated 20% of female workers as 1.2x of 75 since in Q we are given:
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

If earlier no of female workers is 75 then do we not need to perform 1.2*75?


Hi adkikani,

Why are you increasing 75 by 20%? If you read the language of the question carefully it implies that in the new population the composition of women increased to 20%. the question does not say that women population increased by 20% of the original women population after addition of 50 people.
in % problems read carefully what is being increased/decreased
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Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

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New post 31 Dec 2017, 10:45
1
Walkabout 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



Current Ratio of Men: Women- \(85: 15 = 17: 3\)

Thus, Initial number of Women \(= \frac{3}{(17+3)} * 500 = 75\)

Required Ratio of Men: Women- \(80: 20 = 4: 1\)

Thus, final number of Women \(= \frac{1}{(4+1)} * (500+50) = 110\)


Therefore, additional women required \(= 110 - 75 = 35\)

Correct answer is Option E.


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