P and Q can do a project in 12 and 12 days respectively. In how many days can they complete 50% of the project if they work together?

Let total work to be done = 12 units

P can complete the work alone in 12 days

=> P's efficiency = $$\frac{12}{12} = 1$$ unit/day

Q can complete the work alone in 12 days

=> Q's efficiency = $$\frac{12}{12} = 1$$ unit/day

(P + Q)'s 1 day's work = 1 + 1 = 2 units/day

=> 50% of the work = $$\frac{50}{100} \times 12 = 6$$ units

$$\therefore$$ Time taken by them together to complete 50% of the work = $$\frac{6}{2} = 3$$ days

=> Ans - (B)