Question : 4 men and 7 women can do work in 8 days. 7 men and 4 women can do the same work in 5 days. Find the number of days in which 8 women can finish the work.
Option 1: 60 days
Option 2: 55 days
Option 3: 40 days
Option 4: 45 days
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Correct Answer: 55 days
Solution :
4 men and 7 women can do 1 unit of work in 8 days.
$⇒4m + 7w = \frac{1}{8}$ ____(i) where $m$ and $w$ are the efficiencies of a man and 1 woman respectively.
7 men and 4 women can do 1 unit of work in 5 days
$⇒7m + 4w = \frac{1}{5}$ ____(ii)
Multiplying the first equation by 7 and the second equation by 4,
$⇒28m + 49w = \frac{7}{8}$ ____(iii)
$⇒28m + 16w = \frac{4}{5}$ ____(iv)
Subtracting the above equation,
$⇒33w = \frac{7}{8} - \frac{4}{5} = \frac{3}{40}$
$⇒w=\frac{1}{11×40}$
$⇒w=\frac{1}{440}$
The work done by 8 women in a day,
$⇒8w=\frac{8}{440}=\frac{1}{55}$
So, the required days = 55 days.
Hence, the correct answer is 55 days.
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