X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 16 days, Y can alone finish that work in:

Answer: Option B

According to the question,
X → 24 days
⇒ Work done by X in 4 days alone = 4 × 1 = 4 units
⇒ Remaining work = 24 - 4 = 20 units
⇒ 20 units done by both together in (16 - 4 days) = 12 days
⇒ Then efficiencies of (X + Y) $$=\frac{\text{work}}{\text{days}}=\frac{20}{12}=\frac{5}{3}=1+\frac{2}{3}$$
⇒ Efficiency of Y = $$\frac{2}{3}$$
⇒ Time taken by Y alone to complete the total work $$=\frac{24}{\frac{2}{3}}=36\text{ days}$$

Alternate solution:
$$\begin{array}{rl}& X\times 20=\left(X+Y\right)\times 12\\ & \frac{X}{X+Y}=\frac{12}{20}\\ & =\frac{3\to \text{Efficiency of }X}{5\to \text{Efficiency of }\left(X+Y\right)}\end{array}$$
Efficiency of Y = 5 - 3 = 2 units/day
Total work = 24 × 3 = 72 units
Total time taken by Y = $$\frac{72}{2}$$ = 36 days