2 women and 5 men can complete a piece of work in 4 days if the same work is completed by 3 women and 6 men will take 3 days to complete and find the time taken by one man and one woman to do the same work?

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36 and 18

18 and 36

20 and 31

None of these

answer is A.

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Detailed Solution

Concept- Assume that one guy will need a certain number of days to complete the entire task, and that one woman will need a different number of days to complete the same task. Create two equations using the two conditions. Find the portion of the work done by the specified number of men and women over the specified number of days, then convert that portion to one unit of work by adding the two values. Solve both equations now.
Let's imagine that one man can finish the entire project in "x" days and one woman can finish it in "y" days. So, in x days, one man completes one unit of work.
Thus, a man can complete

the amount of work in 1 day.
In a similar vein, a woman can complete

of work in 1 day.
The fact that two women and five men can finish one unit of work in four days fulfils the first criteria. As a result, two women can complete

worth of

labour in a single day instead of only one. As a result, 2 women can complete

of work in 4 days.
As one man can complete

unit of work in one day, five men can complete

amount of work in four days.
Now, we can write the equation as follows: Men's work + Women's work = 1.
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The second condition, which states that the work will be completed in 3 days by 3 women and 6 men, allows us to derive another equation.
Thus, the

work will be completed in three days by three ladies. And in 3 days, 6 men will complete

of the task. So, another equation would be: Amount of labour done by males plus Amount of work done by women Equals 1.
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In order to solve equations (i) and (ii) , set

and

So, we obtain

Equation (iii) can now be expressed as,
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