Q. 24.4( 30 Votes )
5 women and 2 men
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)
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.
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