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In a acertain company, the ratio of the numer of manager to

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Gacarva
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In a acertain company, the ratio of the numer of manager to [#permalink] New post   20 Sep 2010, 19:40
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In a acertain company, the ratio of the numer of manager to the number of production-line workers is 5 to 72. If 8 additional Production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25
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D
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Bunuel
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Re: Ratio PS Manager Production line worker [#permalink] New post   20 Sep 2010, 21:30
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Gacarva wrote:
In a acertain company, the ratio of the numer of manager to the number of production-line workers is 5 to 72. If 8 additional Production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25


You can solve this problem the way discussed above or try the following:

Given: \(\frac{m}{w}=\frac{5x}{72x}\), now 8 workers were hired and new ratio became \(\frac{m}{w+8}=\frac{5x}{74x}=\frac{5x}{72x+2x}\), notice that nominator didn't change, so increase by 2 parts in denominator corresponds to increase by 8 workers (2 parts correspond to 8 workers = 4 times or in another words 2x=8 --> x=4), so 5 parts in nominator correspond to 5*4=20 managers.

Answer: D.
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Re: Ratio PS Manager Production line worker [#permalink] New post   20 Sep 2010, 19:44
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Gacarva wrote:
In a acertain company, the ratio of the numer of manager to the number of production-line workers is 5 to 72. If 8 additional Production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25


Let there be x managers. Then the number of workers is 72/5 * x
With extra workers the ratio becomes 5 to 74, therefore :

\(\frac{(72/5)x + 8}{x}=\frac{74}{5}\)

\(72x + 40 = 74x\)

\(x = 20\)

Answer is (d)
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Re: In a acertain company, the ratio of the numer of manager to [#permalink] New post   07 Sep 2017, 07:09
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Gacarva wrote:
In a acertain company, the ratio of the numer of manager to the number of production-line workers is 5 to 72. If 8 additional Production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25


We are given that the ratio of managers to production-line workers is 5 to 72, or 5x to 72x. We can create the following equation:

(5x)/(72x + 8) = 5/74

74(5x) = (72x + 8)(5)

370x = 360x + 40

10x = 40

x = 4

The company has 4 x 5 = 20 managers.

Answer: D
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company [#permalink] New post   05 Feb 2012, 01:24
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let manager=m , and worker =w
m/w=5/72
=5w=72m.....1
m/w+8=5/74
5w+40=74m...........2
by solving the equations.....we find m=20
so ans is D
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Re: In a acertain company, the ratio of the numer of manager to [#permalink] New post   02 Mar 2018, 04:49
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Bunuel wrote:
Gacarva wrote:
In a acertain company, the ratio of the numer of manager to the number of production-line workers is 5 to 72. If 8 additional Production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25


You can solve this problem the way discussed above or try the following:

Given: \(\frac{m}{w}=\frac{5x}{72x}\), now 8 workers were hired and new ratio became \(\frac{m}{w+8}=\frac{5x}{74x}=\frac{5x}{72x+2x}\), notice that nominator didn't change, so increase by 2 parts in denominator corresponds to increase by 8 workers (2 parts correspond to 8 workers = 4 times or in another words 2x=8 --> x=4), so 5 parts in nominator correspond to 5*4=20 managers.

Answer: D.


Hi Bunuel :-)

can please explain whats wrong with my solution and why :?

let manager be \(y\)

let line worker production be \(x\)

\(\frac{5y}{72x+4}\) =\(\frac{5y}{74x}\) cross multiply

\(360xy+20y=370xy\)

\(20y=370xy-360xy\)

\(20y=10xy\)
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Re: In a acertain company, the ratio of the numer of manager to [#permalink] New post   09 Mar 2018, 12:02
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dave13 wrote:
Bunuel wrote:
Gacarva wrote:
In a acertain company, the ratio of the numer of manager to the number of production-line workers is 5 to 72. If 8 additional Production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25


You can solve this problem the way discussed above or try the following:

Given: \(\frac{m}{w}=\frac{5x}{72x}\), now 8 workers were hired and new ratio became \(\frac{m}{w+8}=\frac{5x}{74x}=\frac{5x}{72x+2x}\), notice that nominator didn't change, so increase by 2 parts in denominator corresponds to increase by 8 workers (2 parts correspond to 8 workers = 4 times or in another words 2x=8 --> x=4), so 5 parts in nominator correspond to 5*4=20 managers.

Answer: D.


Hi Bunuel :-)

can please explain whats wrong with my solution and why :?

let manager be \(y\)

let line worker production be \(x\)

\(\frac{5y}{72x+4}\) =\(\frac{5y}{74x}\) cross multiply

\(360xy+20y=370xy\)

\(20y=370xy-360xy\)

\(20y=10xy\)



It's because you are saying that the ratio is not 5 to 74. You are saying that managers are y and workers are x, you can say that but when you go to solve the problem you are saying that the ratios are 5y:74x thus the resolution is not correct.

Hope it's clear!
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Re: In a acertain company, the ratio of the numer of manager to [#permalink] New post   03 Jun 2021, 11:13
Managers/ PLW= 5/72
new ratio= 5/74 after adding 8 PLW
5x/72x+8=5/74
x= 4
therefore Managers= 5*x= 5*4= 20

therefore D
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Re: In a acertain company, the ratio of the numer of manager to [#permalink] New post   08 Dec 2022, 09:55
m/p = 5/72 ---1)
m/(p+8) = 5/74 --- 2)
putting values for p from 1) in 2)
m/(72m/5 + 8) = 5/74
cross multiplying
74m = 72m + 40
2m = 40
--> m = 20
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Re: In a acertain company, the ratio of the numer of manager to [#permalink] New post   18 Dec 2023, 10:23
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