A does half as much work as B in 1/6th of the time. If together they take 10 days to complete a work, then how much time shall B take to do it alone ?

40

Let B takes x days to complete the work 

According to question , 

Time taken by A to complete the work = 2 × \(\frac{1x}{6}\) =  \(\frac{x}{3}\)

Together they can finish a piece of work in 10 days . 

( A + B )'s 1 day work = \(\frac{1}{10}\)

Now ,  \(\frac{1}{x}\)  +  \(\frac{3}{x}\) = \(\frac{1}{10}\)

x = 40 

Hence B takes 40 days to complete the work