P can finish a work in 18 days. When he had worked for 5 days, Q joined him. If both of them together completed the remaining work in $$\frac{{13}}{5}$$ days, then in how many days can Q alone finish $$66\frac{2}{3}\% $$  of the same work?

$$\eqalign{ & {\text{Total work}} = 18P = 5P + \frac{{13}}{5}\left( {P + Q} \right) \cr & 13P = \frac{{13}}{5}P + \frac{{13}}{5}Q \cr & \frac{{52}}{5}P = \frac{{13}}{5}Q \cr & \frac{P}{Q} = \frac{1}{4} \cr & {\text{Total work}} = 18 \times 1 = 18 \cr & 66\frac{2}{3}\% {\text{ of work}} = \frac{2}{3} \times 18 = 12 \cr & Q{\text{ days}} = \frac{{12}}{4} = 3{\text{ days}} \cr} $$