Question : 3 men and 5 women can do work in 14 days while 5 men can do it in 14 days. 5 men and 5 women can complete the work in _______.
Option 1: 13 days
Option 2: 11 days
Option 3: 10 days
Option 4: 12 days
Correct Answer: 10 days
Solution :
5 men can do 1 work in 14 days.
3 men will do $\frac{3}{5}$ work in 14 days.
Remaining work $= 1-\frac{3}{5}= \frac{2}{5}$
5 women do $\frac{2}{5}$ work in 14 days.
Time taken by 5 women to do the whole work $= \frac{14 \times 5}{2}= 35$ days
5 men + 5 women's 1 day work $=\frac{1}{14}+\frac{1}{35}=\frac{5+2}{70}=\frac{7}{70}=\frac{1}{10}$
∴ Required time = 10 days.
Hence, the correct answer is 10 days.
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