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.]
