P and Q together can do a work in 12 days. P alone can do the same work in 36 days. In how many days can Q alone complete two third part of same work?

12

P + Q = 12 days,

P = 36 days,

⇒ Simplifying, we can get that Q = 2     (Efficiency)

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

⇒ Time required for Q alone to complete 24 units =  \(\frac{24}{2}\) = 12 days.     ..(\(\frac{Work}{Efficiency}\) = Time)