Question : 15 men and 21 women working together can do a job in 56 days, while 12 men and 24 women working together can do the same job in 64 days. In how many days can the same job be done by 18 men and 24 women working together?
Option 1: $47\frac{6}{19}$
Option 2: $47\frac{5}{19}$
Option 3: $47\frac{9}{19}$
Option 4: $47\frac{3}{19}$
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Correct Answer: $47\frac{3}{19}$
Solution :
Given:
15 men and 21 women can do a piece of work in 56 days.
12 men and 24 women can do it in 64 days.
Let the efficiency of 1 man is $x$ and 1 woman's efficiency is $y$.
So, $(15x+21y)×56=(12x+24y)×64$
⇒ $840x+1176y=768x+1536y$
⇒ $72x=360y$
⇒ $\frac{x}{y}=\frac{5}{1}$
Let the total work = $(15×5+21×1)×56=5376$ units.
So, (18 men + 24 women)'s efficiency is $18×5+24×1=114$
Therefore, they will do the work in $\frac{5376}{114}=\frac{896}{19}=47 \frac{3}{19}$ days.
So, 18 men and 24 women working together will finish the job in $47 \frac{3}{19}$ days
Hence, the correct answer is $47 \frac{3}{19}$.
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