A does half as much work as B in one-sixth of the time. If together they take 10 days to complete a work. How much time shall B alone take to do it ?

Suppose B takes x days to do the work.
$$\eqalign{ & {\text{A takes}} = \left( {2 \times \frac{1}{6}x} \right) \cr & = \frac{1}{3}x{\text{ days to do it}}{\text{.}} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} = \frac{1}{{10}} \cr & \Rightarrow \frac{1}{x} + \frac{3}{x} = \frac{1}{{10}} \cr & \Rightarrow \frac{4}{x} = \frac{1}{{10}} \cr & \Rightarrow x = 40{\text{ days}}{\text{.}} \cr} $$