A completes $$\frac{7}{{10}}$$ of the work 15 days. Then he completes the remaining work the help of B in 4 days. The time required for A and B together to complete the entire work is = ?

$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 4 day's work}} \cr & = \left( {1 - \frac{7}{{10}}} \right) \cr & = \frac{3}{{10}} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{3}{{10}} \times \frac{1}{4}} \right) \cr & = \frac{3}{{40}} \cr & {\text{Remaining work }} \cr & = \left( {1 - \frac{3}{{10}}} \right) \cr & = \frac{7}{{10}}{\text{ }} \cr & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{15}} + \frac{1}{{20}}} \right) \cr & = \frac{7}{{60}} \cr} $$
Hence, A an B together take $$ = \frac{{40}}{3} = 13\frac{1}{2}$$   days to complete the entire work.