A, B and C can separately do a work in 12, 15 and 20 days respectively. They started to work together but C left after 2 days. The remaining work will be finished in = ?

Solution(By Examveda Team)

$$\eqalign{ & \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{12}} + \frac{1}{{15}} + \frac{1}{{20}}} \right) \cr & = \frac{{12}}{{60}} \cr & = \frac{1}{5} \cr & \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 2 day's work}} \cr & = \left( {\frac{1}{5} \times 2} \right) \cr & = \frac{2}{5} \cr & {\text{Remaining work }} \cr & = \left( {1 - \frac{2}{3}} \right) \cr & = \frac{3}{5}{\text{ }} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{12}} + \frac{1}{{15}}} \right) \cr & = \frac{9}{{60}} = \frac{3}{{20}} \cr & {\text{Now, }}\frac{3}{{20}}{\text{ work is done by A and B in 1 day}} \cr & \therefore \frac{3}{5}\,{\text{work is done by A and B in }} \cr & = \left( {\frac{{20}}{3} \times \frac{3}{5}} \right) \cr & = 4{\text{ days}}{\text{.}} \cr} $$