2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman as well as 1 man to finish the work if each of them works alone.

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Time taken by 1 woman alone to finish the work: 24 days, and also that taken by 1 man alone: 32 days

Time taken by 1 woman alone to finish the work: 18 days, and also that taken by 1 man alone: 36 days

Time taken by 1 woman alone to finish the work: 14 days, and also that taken by 1 man alone: 30 days

Time taken by 1 woman alone to finish the work: 12 days, and also that taken by 1 man alone: 28 days

answer is B.

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Detailed Solution

Concept- Time and work have been concerned with the amount of time it takes an individual or a group of individuals to complete a piece of work and the efficiency with which each of them completes it.
Consider the work done by man and woman per day as

and

respectively.
As since 5 men and 2 women complete the work in 4 days,
The work done by 5 men and 2 women in 1 day

…..(1)
As since 6 men and 3 women complete the work in 3 days,
The work done by 6 men and 3 women in 1 day

….(2)
When multiplying (1) by 3, we get

…..(3)
When multiplying (2) by 2, we get

…..(4)
When subtracting (4) from (3), we get

When substituting the value of

in (2), we get

So, work done by 1 man in 1 day

days
Thus, the time taken by 1 man alone to finish the work

days
Now, work done by 1 woman in 1 day

days
Therefore, the time taken by 1 woman alone to finish the work