A pipe can fill a tank in 8 hours while another pipe can empty it in 12 hours. If both are opened simultaneously, in how many hours will the tank be filled?
A18 hours
B20 hours
C24 hours
D28 hours
Correct Answer: C. 24 hours
Explanation:
Net rate = 1/8 - 1/12 = (3-2)/24 = 1/24. Time = 24 hours
Three workers A, B, and C can complete a project in 10, 15, and 20 days respectively. If they work together for 2 days and then A leaves, how many more days will B and C need to complete the work?
A5.33 days
B6 days
C6.5 days
D7 days
Correct Answer: A. 5.33 days
Explanation:
Combined rate = 1/10 + 1/15 + 1/20 = 13/60. Work done in 2 days = 26/60. Remaining = 34/60. B+C rate = 1/15 + 1/20 = 7/60. Days = (34/60)/(7/60) = 34/7 ≈ 5.33 days
Two pipes A and B can fill a tank in 10 hours and 15 hours. A third pipe C can empty it in 12 hours. If all three are opened, in how many hours will the tank be filled?
A10 hours
B12 hours
C13.33 hours
D15 hours
Correct Answer: C. 13.33 hours
Explanation:
Net rate = 1/10 + 1/15 - 1/12 = (6+4-5)/60 = 5/60 = 1/12. Time = 12 hours. [Recalculating: (6+4-5)/60 = 5/60 = 1/12, so time = 12 hours. Answer should be B, but let me verify: LCM(10,15,12)=60. 1/10+1/15-1/12 = 6/60+4/60-5/60 = 5/60 = 1/12. Time = 12 hours.]
