Pipes A and B can fill a tank in 18 hours and 24 hours, respectively, while pipe C alone can empty the full tank in 30 hours. Pipes A and B are opened together for 6 hours, and then A is closed and C is opened instantly (with B). After closing pipe A, how much time (in hours) will B and C together take to fill the tank completely?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 50.
Combined rate of A and B = 1/18 + 1/24 = 7/72
Filled in 6 hours = 6 × (7/72) = 7/12
Remaining = 1 - 7/12 = 5/12
After 6 hours, A is closed, C is opened (with B still open)
Combined rate (B + C) = 1/24 - 1/30 = 1/120 (net filling rate)
Time required to fill the remaining = (5/12)/(1/120) = 50 hours