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# A manufacturing company employs staff.work full or part time

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A manufacturing company employs staff.work full or part time [#permalink]  23 Jan 2011, 01:57
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Q) A manufacturing company employs staff who work either on full time basis or on part time basis. The ratio of number of males who work on part time basis to the number of males who work on full time basis is 4 to 5.And the ratio of number of females who work on part time basis to the number of males who work on part time basis is 3 to 2.If the ratio of the number of females who work on full time basis to the number of males who work on full time basis is 3:1, what is the ratio of number of females who work on part time basis to the number of females who work on full time basis ?

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Re: A manufacturing company employs staff.work full or part time [#permalink]  23 Jan 2011, 03:19
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MichelleSavina wrote:
Q) A manufacturing company employs staff who work either on full time basis or on part time basis. The ratio of number of males who work on part time basis to the number of males who work on full time basis is 4 to 5. And the ratio of number of females who work on part time basis to the number of males who work on part time basis is 3 to 2. If the ratio of the number of females who work on full time basis to the number of males who work on full time basis is 3:1, what is the ratio of number of females who work on part time basis to the number of females who work on full time basis ?

The ratio of number of males who work on part time basis to the number of males who work on full time basis is 4 to 5: $$\frac{male_p}{male_f}=\frac{4}{5}$$;

The ratio of number of females who work on part time basis to the number of males who work on part time basis is 3 to 2: $$\frac{female_p}{male_p}=\frac{3}{2}=\frac{6}{4}$$, so from above: $$\frac{female_p}{male_f}=\frac{6}{5}$$ --> $$male_f=\frac{5*female_p}{6}$$;

The ratio of the number of females who work on full time basis to the number of males who work on full time basis is 3:1: $$\frac{female_f}{male_f}=\frac{3}{1}$$ --> $$\frac{female_f}{\frac{5*female_p}{6}}=\frac{3}{1}$$ --> $$\frac{female_p}{female_f}=\frac{2}{5}$$.
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Re: A manufacturing company employs staff.work full or part time [#permalink]  23 Jan 2011, 03:38
MichelleSavina wrote:
A manufacturing company employs staff who work either on full time basis or on part time basis. The ratio of number of males who work on part time basis to the number of males who work on full time basis is 4 to 5.And the ratio of number of females who work on part time basis to the number of males who work on part time basis is 3 to 2.If the ratio of the number of females who work on full time basis to the number of males who work on full time basis is 3:1, what is the ratio of number of females who work on part time basis to the number of females who work on full time basis ?

Say,
Number of part-time male = m
Number of full-time male = M
Number of part-time female = f
Number of full-time female = F

Hence,
m:M = 4:5 => m = (4M/5) => M = (5m/4)
f:m = 3:2 => f = (3m/2)
F:M = 3:1 => F = 3M = (15m/4)

Therefore, $$\frac{f}{F} = (\frac{3m}{2})/(\frac{15m}{4}) = \frac{3}{2}*\frac{4}{15} = \frac{2}{5}$$
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Re: A manufacturing company employs staff.work full or part time   [#permalink] 23 Jan 2011, 03:38
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