Two pipes A and B can fill a tank in 10 and 12 hours, respectively, and a…

Step-by-Step Solution

To solve this, we determine the status of the tank step-by-step based on which pipes are active.

1. Define Pipe Rates:

   • Pipe A (filling): 1/10 tank/hour

   • Pipe B (filling): 1/12 tank/hour

   • Pipe C (emptying): 1/4 tank/hour

2. Calculate Cumulative Fill Status by 9 a.m.:

   • From 6 a.m. to 7 a.m. (1 hour): Only A is open.

     • Work done = 1/10

   • From 7 a.m. to 9 a.m. (2 hours): A and B are open.

     • Combined rate = 1/10 + 1/12 = (6+5)/60 = 11/60 tank/hour.

     • Work done = (11/60) * 2 = 11/30

   • Total filled by 9 a.m.: 1/10 + 11/30 = 3/30 + 11/30 = 14/30 = 7/15.

3. Calculate Net Rate from 9 a.m. onwards:

   • When A, B, and C are all open:

   • Net rate = (1/10 + 1/12) - 1/4

   • Net rate = (11/60) - 15/60 = -4/60 = -1/15.

   • Since the rate is negative, the tank is emptying at a rate of 1/15 tank/hour.

4. Find Time to Empty:

   • Tank to be emptied = 7/15.

   • Time required = (7/15) / (1/15) = 7 hours.

5. Determine Final Time:

   • Starting from 9 a.m., adding 7 hours gives 4 p.m.