A can finish a work in 18 days and B can do the same work in half the time take by A. Then, working together, what part of the same work they can finish in a day ?

$$\eqalign{ & {\text{A's 1 day's work}} = \frac{1}{{18}} \cr & {\text{And}} \cr & {\text{B's 1 day's work}} = \frac{1}{9} \cr & \therefore \left( {{\text{A}} + {\text{B}}} \right)'{\text{s 1 day's work}} \cr & = \left( {\frac{1}{{18}} + \frac{1}{9}} \right) \cr & = \frac{1}{6} \cr} $$