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 ?

Answer: Option C

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