Question

36 men can do a project work in X days and the 24 women can do same project in (X+13) days. if the amount of work done by 42 men in one day to the work done by 18 women in one day is 3:1
what is the value of X?

Answer 1

Amount of work done per man per day = 1/(36X)
Amount of work done per woman per day = 1/[24(X+13)]

Amount of work done by 42 men per day = 42/36X --------------------------- a
Amount of work done by 18 women per day = 18/[24(X+13)]--------------- b

As per the relation given in the problem statement the ratio of a:b is 3:1

Which implies (42/36X)/[18/(24(X+13))] = 3/1

Simplifying this would give you X = 14.