5 women and 2 men together can finish an embroidery work in 4 days, while 6 women and 3 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work. Also find the time taken by 1 man alone to finish the work.

Let W and M represent the work done by a woman and a man respectively.

It is given that 5 women and 2 men can do the work in 4 days.

So, work done by 5 women and 2 men in a day will be

⇒ 20W + 8M = 1 …. (i)

Also,

It is given that 6 women and 3 men can do the same work in 3 days.

So, work done by 6 women and 3 men in a day will be

⇒ 18W + 9M = 1 …. (ii)

From (i) and (ii) equation,

20W + 8M = 18W + 9M

⇒ 2W = M

This means that the work done by 2 women in a day is equal to the work done by a man in a day. Substituting the value of M in (i) equation, we get

20W + 8M = 1

⇒ 20W + 8× 2W = 1

⇒ (20 + 16) W = 1

So, a woman do work in a day.

This means a woman will finish the work in 36 days if working alone.

Now, put the value of W in (ii),

18W + 9M = 1

So, a man do work in a day.

This means a man will finish the work in 18 days if working alone.