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?
A. 3
B. 5
C. 7
D. Cannot be determined
E. None of these

Answer 1

Hint: Start by finding the amount of work women and children can do in a certain number of days, so that we can find a relation between their efficiency or manpower . After that, find out work done by each group in 1 day, using this try to find out work done by 5 women and 10 children in 1 day which would eventually give us how many days they would take to complete the work.

Complete step-by-step answer:
We are given that the number of days 10 women can complete the work = 7 days
And number of days 10 children can complete the work = 14 days
As both are doing the same amount of work,
We can conclude that 70 women’s work = 140 children’s work
Or we can say ${\text{1 women }} \equiv {\text{ 2 children}}$in terms of efficiency.
Now , The work done by 10 women in 7 days
= ${\text{Number of women}} \times {\text{ Number of days worked}}$
$ = 10 \times 70 = 70$
Similarly , Work done by 10 children in 14 days
=${\text{Number of children}} \times {\text{ Number of days worked}}$
$ = 10 \times 14 = 140$
Now we will find the number of days required by 5 women and 10 children to complete the work.
Work done by 1 woman in 1 day = $\dfrac{1}{{70}}$
Work done by 1 child in 1 day = $\dfrac{1}{{140}}$
Now we need to find the number of days required by 5 women and 10 children to complete the work. So for that we’ll find out the work done by them in 1 day.
Work done by 5 women and 10 children in 1 day $ = \dfrac{5}{{70}} + \dfrac{{10}}{{140}}$
$
   = \dfrac{1}{{14}} + \dfrac{1}{{14}} \\
   = \dfrac{1}{7} \\
$
$\because $Together they complete $\dfrac{1}{7}th$ of the task in a day , which means they would take 7 days to complete it.
$\therefore $5 women and 10 children will complete the work in 7 days.

So, the correct answer is “Option C”.

Note: While solving this question, one can get confused in calculating the number of days by work done of each woman and each child. We can also use another way i.e. convert the number of women into number of children i.e.1 women = 2 children and then calculate number of days by children’s work done which will also be equal to work done by 5 women and 10 children.