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 C

$$\begin{array}{rl}& \text{X’s 1 day’s work}=\frac{1}{24}\\ & \text{X’s 16 day’s work}=\frac{16}{24}\\ & \text{Let,}\end{array}$$
Y alone complete the work in x days
$$\text{Y’s 12 day’s work}=\frac{12}{x}$$
According to the question,
Complete work done by X and Y = 1
X's 16 day's work + Y's 12 day's work = 1
$$\begin{array}{rl}& \Rightarrow \frac{16}{24}+\frac{12}{x}=1\\ & \Rightarrow \frac{2}{3}+\frac{12}{x}=1\\ & \Rightarrow \frac{12}{x}=1-\frac{2}{3}=\frac{1}{3}\\ & \Rightarrow x=12\times 3\\ & \Rightarrow x=36\text{ days}\end{array}$$