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20 Sep 2010, 19:40
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D
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Difficulty:
15%
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Question Stats:
86% (01:46) correct
14%
(02:18)
wrong
based on 1738
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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
A. 5
B. 10
C. 15
D. 20
E. 25
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.
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.
20 Sep 2010, 19:44
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Gacarva
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)
