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A manufacturing company employs staff.work full or part time

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Joined: 27 Sep 2010
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A manufacturing company employs staff.work full or part time  [#permalink]

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23 Jan 2011, 02:57
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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]

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23 Jan 2011, 04:19
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]

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23 Jan 2011, 04:38
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]

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20 Mar 2016, 07:39
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 ?

Mp =Male part time, Fp= female part time, Mf= male full time, Ff= female full time
Given,
Mp/Mf=4/5---------------(1)
Fp/Mp=3/2-----------------(2)
Ff/Mf=3/1-----------------(3)
Fp/Ff=? = (2)*(1)/(3) = 2:5
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Re: A manufacturing company employs staff.work full or part time  [#permalink]

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26 Sep 2018, 05:34
We can even solve this question using the 2 variable Table approach.

Where
pt is Part Time job
ft is Part Time job

Since we are given ratios we can take apt values to give us those values.

1) 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
M pt : M ft = 40:50

2) 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
F pt : M pt = 60:40

3) 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,
F ft : M ft = 150:50

To Find the ratio of number of females who work on part time basis to the number of females who work on full time basis

F pt : F ft = 60 : 150
F pt : F ft = 2: 5

Table Representation for the same

M F Total
PT 40 60 100
FT 50 150 200
Total 90 120 300

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Re: A manufacturing company employs staff.work full or part time   [#permalink] 26 Sep 2018, 05:34
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