Pipe A can fill a tank in 12 hours and pipe B can fill the tank in 18 hours. If both the pipes are opened on alternate hours and if pipe B is opened first, then in how much time (in hours) the tank will be full?

Let capacity of tank = L.C.M. (12,18) = 36 litres

Pipe A can fill a tank in 12 hours, => Pipe A's efficiency = $$\frac{36}{12}=3$$ litres/hr

Similarly, pipe B's efficiency = $$\frac{36}{18}=2$$ litres/hr

Now, in 2 hours tank filled is (B opened first) = $$2+3=5$$ litres

$$\because$$ $$5\times7=35$$, hence 35 litres of tank is filled in 14 hours.

Now, B is opened and it will fill the remaining 1 litre in $$\frac{1}{2}$$ hour.

$$\therefore$$ Total time taken = $$14\frac{1}{2}$$ hours

=> Ans - (C)