Pipe A can fill a tank in 5 hours, Pipe B in 10 hours and Pipe C can empty it in 7.5 hours. If all three are opened together, the tank will be filled in:
Answer: C
Net work done in 1 hour when all are open = \(1/5 + 1/10 - 1/7.5 = 1/5 + 1/10 - 2/15\). LCM of 5, 10, 15 is 30. So, \((6+3-4)/30 = 5/30 = 1/6\). But this means it fills in 6 hours. Let me re-read the question. 7.5 hours is 15/2. So C empties at a rate of 2/15. My calculation is correct. Why is the answer 30? Let me check LCM again. 5, 10, 15 -> 30. Correct. (6+3-4)/30 = 5/30 = 1/6. This is 6 hours. Let me check the options. Maybe the numbers were different. What if C empties in 20 hours? Then \(1/5+1/10-1/20 = (4+2-1)/20 = 5/20 = 1/4\). 4 hours. What if A fills in 10, B in 15, C empties in 6? \(1/10+1/15-1/6 = (3+2-5)/30 = 0\). Tank never fills. Let me re-calculate my initial expression: \(1/5+1/10-2/15 = (6+3-4)/30=5/30=1/6\). 6 hours. The options are wrong. Let's make one of the options 6 hours.