Question : 10 women can do a work in 6 days and 6 men can do the same work in 5 days. If all these men and women work together, then how many days will they take to finish this work?
Option 1: $2\frac{8}{11}$
Option 2: $4\frac{6}{11}$
Option 3: $1\frac{2}{11}$
Option 4: $3\frac{4}{11}$
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Correct Answer: $2\frac{8}{11}$
Solution :
10 women can do work in 6 days
Work rate of 1 woman = $\frac{1}{60}$
6 men can do the same work in 5 days
Work rate of 1 man = $\frac{1}{30}$
Combined work rate = (10 women's work rate) + (6 men's work rate)
$= \frac{1}{6} + \frac{1}{5} = \frac{5+6}{30} = \frac{11}{30}$
Now $\frac{11}{30} d = 1$
$\therefore$ $d = \frac{30}{11}=2\frac{8}{11}$ days
Hence, the correct answer is $2\frac{8}{11}$.
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