A can do half as much work as B in 3/4th of the time. Together they can finish a piece of work in 18 days. In how many days will B alone finish the work ?

30

Let B takes x days to complete the work 

According to question , 

time taken by A to complete the work = 2 × \(\frac{3x}{4}\) =  \(\frac{3x}{2}\)

Together they can finish a piece of work in 18 days . 

( A + B )'s 1 day work = \(\frac{1}{18}\)

Now ,  \(\frac{1}{x}\)  +  \(\frac{2}{3x}\) = \(\frac{1}{18}\)

x = \(\frac{18 \;× \;5}{3}\) = 30 

Hence B takes 30 days to complete the work