Pipes P and Q can fill a water tank in 10 hours and 15 hours, respectively. A pipe R can empty a tank filled with water in 12 hours. Initially, the tank is empty and only pipes P and Q are opened at 6 a.m. and pipe R is also opened at 9 a.m. By what time will the tank be filled?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 3 p.m..
Pipes P and Q can fill a water tank in 10 hours and 15 hours, respectively. A pipe R can empty a tank filled with water in 12 hours.
L.C.M(10, 15, and 12) = 60
The efficiency of Pipe P = 60/10 = 6 units
The efficiency of Pipe Q = 60/15 = 4 units
The efficiency of Pipe R = 60/12 = -5 units [-ve sign because it empties the tank]
Only pipes P and Q were opened at 6 a.m. and they worked for 3 hours
⇒ 3 × (6 + 4)
⇒ 3 × 10 = 30 units
Remaining units = 60 - 30 = 30 units
Now, all three pipes are open and their efficiency is (6 + 4 - 5) = 10 - 5 = 5 units
Time taken = 30/5 = 6 hrs
Total time = 3 + 6 hrs = 9 hours
So, the tank will be filled = 6 a.m. + 9hrs = 3 p.m.