A, B and C can complete a work in 10, 12 and 15 days respectively. They started the work together. But A left the work 5 days before its completion. B also left the work 2 days after A left. In how many days was the work completed ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{C's 3 day's work}} \cr & = \left( {\frac{1}{{15}} \times 3} \right) \cr & = \frac{1}{5} \cr & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 2 day's work}} \cr & = \left[ {\left( {\frac{1}{{12}} + \frac{1}{{15}}} \right) \times 2} \right] \cr & = \left( {\frac{3}{{20}} \times 2} \right) \cr & = \frac{3}{{10}} \cr & \therefore {\text{Remaining work}} \cr & = \left[ {1 - \left( {\frac{1}{5} + \frac{3}{{10}}} \right)} \right] \cr & = \left( {1 - \frac{1}{2}} \right) \cr & = \frac{1}{2} \cr & \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{10}} + \frac{1}{{12}} + \frac{1}{{15}}} \right) \cr & = \frac{{15}}{{60}} \cr & = \frac{1}{4} \cr} $$
$$\frac{1}{4}$$ work is done by A, B ans C in 1 day.
∴ $$\frac{1}{2}$$ work is done by A, B and C in
$$\eqalign{ & = \left( {4 \times \frac{1}{2}} \right) \cr & = {\text{2 days}} \cr & {\text{Total number of days}} \cr & = \left( {3 + 2 + 2} \right) \cr & = 7 \cr} $$