Answer :

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.


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