P and Q together can do a work in 12 days. P alone can do the same work in 18 days. In how many days can Q alone complete two third part of the same work?

24

P + Q = 12 days,

P = 18 days,

⇒ So, Q in a day = 1   (Efficiency) 

⇒ \(\frac{2}{3}\) of total work = \(\frac{2}{3}\) x 36 = 24 units.

⇒ Time taken by Q to complete 24 units of work = \(\frac{24}{1}\) = 24 days.  ..(\(\frac{Work}{Efficiency}\) = Time )