A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

$$\eqalign{ & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{15}}; \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{20}}; \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1day's}}\,{\text{work}} \cr & = {\frac{1}{{15}} + \frac{1}{{20}}} = \frac{7}{{60}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{4}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{7}{{60}} \times 4} = \frac{7}{{15}} \cr & \therefore {\text{Remaining}}\,{\text{work}}\, = {1 - \frac{7}{{15}}} = \frac{8}{{15}} \cr} $$