A and B can separately do a work in 6 days & 18 days. They worked together for 3 days after which

B was replaced by C. If the work was finished in next 5/3 days, the number of days in which C alone could do the work is

A can do work in  1 day $=\frac{1}{6}$

B can do work in  1 day $=\frac{1}{18}$

Together work for  3 days $\Rightarrow [\frac{1}{6}+\frac{1}{18}]\times 3\Rightarrow \frac{4}{18}\times 3=\frac{2}{3}work$

Remaining work $=\frac{1}{3}donebyA\&C$

C can complete the work in X days.

A & C's one day work = $\frac{1}{6}+\frac{1}{x}=\frac{6+x}{6x}$

A & C can complete the total work in $\frac{6x}{6+x}$days

A & C can complete $\frac{1}{3}rd$work in $\frac{5}{3}$days

$$\begin{gathered} \Rightarrow \frac{1}{3}\times \frac{6x}{6+x}=1\times \frac{5}{3} \\ \Rightarrow 6x=30+5x \\ \Rightarrow x = 30 \end{gathered}$$