Let number of days B required a work be x

Then number of days A takes to complete the work is : = 1.5x

Work done by A in one day: =

Work done by B in one day:

Number of days taken by A and B to do the work together: 18 days

Work done by A and B together in one day:

That is : = +

=

X = = 30

B alone will take 30 days to complete the work.