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 ?

$$\eqalign{ & {\text{X's 1 day's work}} = \frac{1}{{24}} \cr & {\text{X's 16 day's work}} = \frac{{16}}{{24}} \cr & {\text{Let,}} \cr} $$
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
$$\eqalign{ & \Rightarrow \frac{{16}}{{24}} + \frac{{12}}{x} = 1 \cr & \Rightarrow \frac{2}{3} + \frac{{12}}{x} = 1 \cr & \Rightarrow \frac{{12}}{x} = 1 - \frac{2}{3} = \frac{1}{3} \cr & \Rightarrow x = 12 \times 3 \cr & \Rightarrow x = 36{\text{ days}} \cr} $$