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Q.

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work[[1]] days.


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Detailed Solution

Concepts: 5 women and 10 children take 7 days to complete the work.
Start by looking for a day's worth of labor for one woman and one child. Then carefully sum the results for 10 children and 5 women separately to arrive at the solution.
So as we know that a work can be completed by 10 women in 7 days so for 10 women in 1 day only  1 7   work will be completed so in one day by 1 women only  1 70   work will be complete.
So, 1 women’s one day’s work = 1 70  
Now for children as we know the work can be completed by 10 children in 14 days so for 10 children in 1 day only  1 14   work will be completed so in one day by one child only 1/140 work will be completed.
So, 1 child one day’s work = 1 140  
Now we are asked about 5 women and 10 children. So, 5 women’s one day work is  5 70   or 1 14  
 and for 10 children’s one day work is  10 140   or 1 14  
Hence by 5 women and 10 children one day work is  1 14 + 1 14 = 1 7   so, total work can be completed by 5 women and 10 children in 7 days.
Hence, the answer is 7 days.
 
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