Question

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?

Answer 1

Hint: At first try to find one women and one child’s one day work. The find separately for 5 women and 10 children and then add them carefully and hence find the answer.

Complete step-by-step answer:
So as we know that a work can be completed by 10 women in 7 days so for 10 women in 1 day only $\dfrac{1}{7}$ work will be completed so in one day by 1 women only $\dfrac{1}{70}$ work will be complete.
So, 1 women’s one day’s work $=\dfrac{1}{70}$
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 $\dfrac{1}{14}$ work will be completed so in one day by one child only $\dfrac{1}{140}$ work will be completed.
So, 1 child one day’s work $=\dfrac{1}{140}$ .
Now we are asked about 5 women and 10 children. So, 5 women’s one day work is $\dfrac{5}{70}or\dfrac{1}{14}$ and for 10 children’s one day work is $\dfrac{10}{140}or\dfrac{1}{14}$ .
Hence by 5 women and 10 children one day work is $\dfrac{1}{14}+\dfrac{1}{14}or\dfrac{1}{7}$ so, total work can be completed by 5 women and 10 children is 7 days.
Hence the answer is 7 days.

Note: Students while doing these kinds of problems should keep what is asked on the right hand side so that calculations can be made easily.
Another approach is 10 Women can complete a work in 7 days and 10 children take 14 days to complete the work.
So, equate this as the work considered here is same, so we get
10 women, 7 days = 10 children, 14 days
Now 10 women work for 7 days so in one day the work will be done by 70 women, similarly 140 children will do the same work in one day, so we get
70 women’s work = 140 children work
From, here work accordingly to get the same answer as above.