Problem: Find the time at which the tank will be emptied if two pipes fill the tank in 15 and 12 hours respectively and a third pipe empties it in 4 hours, and the pipes are opened in order at 8,9 and 11 a.m. respectively.

Solution:
To solve this problem, we need to find how much water is filled in the tank and how much is emptied during the given time intervals.

Filling of Tank:
Let the capacity of the tank be 'C' units.
Let the rate of filling of first pipe be 'F1' units per hour.
Let the rate of filling of second pipe be 'F2' units per hour.
Let the time duration for which the first pipe is opened be 'T1' hours.
Let the time duration for which the second pipe is opened be 'T2' hours.
Using the formula, Amount of water filled = Rate of filling x Time duration, we get:
Amount of water filled by first pipe = F1 x T1
Amount of water filled by second pipe = F2 x T2
Total amount of water filled = F1 x T1 + F2 x T2
Given,
F1 = C/15 units per hour
F2 = C/12 units per hour
T1 = 1 hour (8 a.m. to 9 a.m.)
T2 = 2 hours (9 a.m. to 11 a.m.)
Substituting the values, we get:
Amount of water filled = (C/15) x 1 + (C/12) x 2
= (C/15) + (C/6)
= (3C + 5C)/60
= 8C/60
= 2C/15 units

Emptying of Tank:
Let the rate of emptying of third pipe be 'E' units per hour.
Let the time duration for which the third pipe is opened be 'T3' hours.
Using the formula, Amount of water emptied = Rate of emptying x Time duration, we get:
Amount of water emptied by third pipe = E x T3
Given,
E = C/4 units per hour
T3 = 1 hour (11 a.m. to 12 p.m.)
Substituting the values, we get:
Amount of water emptied = (C/4) x 1
= C/4 units

Net Amount of Water:
Net amount of water in the tank after opening all the pipes in order is:
Net amount = Amount of water filled - Amount of water emptied
= 2C/15 - C/4
= (8C - 15C)/60
= -7C/60 units
(Note: Negative sign indicates that the tank is emptied.)

Time to Empty the Tank:
Let the time taken to empty the tank be 'T' hours.
Using the formula, Net amount of water = Rate of emptying x Time duration, we get:
Net amount of water = -C/T units
Substituting the values, we get:
-C/T = -7C/60
T = 60/7 hours
= 8 hours and 34 minutes
Therefore, the tank will be emptied at approximately 8:34 p.m.

Conclusion: