X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

Answer: Option A

Work done by X in 8 days = $$\frac{1}{40}\times 8$$   = $$\frac{1}{5}$$
Remaining work = $$1-\frac{1}{5}$$   = $$\frac{4}{5}$$
Now, $$\frac{4}{5}$$ work is done by Y in 16 days
Whole work will be done by Y in = $$16\times \frac{5}{4}$$   = 20 days
∴ X's 1 day's work = $$\frac{1}{40}$$
∴ Y's 1 day's work = $$\frac{1}{20}$$
(X + Y)'s 1 day's work
$$\begin{array}{rl}& =\frac{1}{40}+\frac{1}{20}\\ & =\frac{3}{40}\end{array}$$
Hence, X and Y will together complete the work in
$$\begin{array}{rl}& =\frac{\text{40}}{\text{3}}\\ & \text{ = 13}\frac{\text{1}}{\text{3}}\text{days}\end{array}$$