A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work. A leaves off. The total number of days to complete the work is ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{B's 3 day's work}} \cr & = \left( {\frac{1}{{21}} \times 3} \right) \cr & = \frac{1}{7} \cr & {\text{Remaining work}} \cr & = \left( {1 - \frac{1}{7}} \right) \cr & = \frac{6}{7} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{14}} + \frac{1}{{21}}} \right) \cr & = \frac{5}{{42}} \cr} $$
Now, $$\frac{5}{{42}}$$ work is done by A and B in 1 day
$$\eqalign{ & \therefore \frac{6}{7}{\text{ work is done by A and B in}} \cr & = \left( {\frac{{42}}{5} \times \frac{6}{7}} \right) \cr & {\text{ = }}\frac{{36}}{5}{\text{ days}} \cr & {\text{Hence, total time taken}} \cr & = \left( {3 + \frac{{36}}{5}} \right){\text{days}} \cr & = 10\frac{1}{5}{\text{days}}{\text{.}} \cr} $$