A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the wall ?

Solution(By Examveda Team)

Part of wall built by A in 1 day = $$\frac{1}{8}$$
Part of wall broken by B in 1 day = $$\frac{1}{3}$$
Part of wall built by A in 4 days
$$\eqalign{ & = \left( {\frac{1}{8} \times 4} \right) \cr & = \frac{1}{2} \cr} $$
Part of wall broken by B and built by A in 2 days
$$\eqalign{ & = 2\left( {\frac{1}{3} - \frac{1}{8}} \right) \cr & = \frac{5}{{12}} \cr} $$
$$\eqalign{ & {\text{Part of wall built in 6 days}} \cr & = \left( {\frac{1}{2} - \frac{5}{{12}}} \right) \cr & = \frac{1}{{12}} \cr & {\text{Remaining part to be built}} \cr & = \left( {1 - \frac{1}{{12}}} \right) \cr & = \frac{{11}}{{12}} \cr} $$
Now, $$\frac{1}{8}$$ part of wall built by A in 1 day
$$\eqalign{ & \therefore \frac{{11}}{{12}}{\text{ part of wall built by A in}} \cr & = \left( {8 \times \frac{{11}}{{12}}} \right) \cr & = \frac{{22}}{3} \cr & = 7\frac{1}{3}{\text{ day}} \cr} $$