A pipe can fill a tank in 10 minutes while another pipe can empty it in 12 minutes. If the pipes are opened alternately each for 1 minute, beginning with the first pipe, the tank will be full after (in minutes):

Let capacity of tank be L.C.M.(10,12) = 60 litres

First pipe can fill it in 10 minutes, => A's efficiency = $$\frac{60}{10}=6$$ litres/min

Similarly, B's efficiency = $$\frac{60}{-12}=-5$$ litres/min

If opened alternatively for 1 minute each, tank filled will be $$(6)+(-5)=1$$ litre in 2 minutes

Now, after 108 minutes, => 54 litres of the tank will be filled, and it will be of A's turn which will fill the remaining  litres in the next minute.

Thus, total time taken is 109 minutes.

=> Ans - (B)