Pipes A and B can fill a tank in 16 hours and 24 hour, respectively. Pipe C can alone empty the full tank in x hours. All the pipes were opened together at 10:30 am, but C was closed at 2:30 pm. If the tank was full at 8:30 pm on the same day, then what is the value of x?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 96.
Efficiency of A = 1/16 units/hour
Work done by A in 10 hours = 10/16 = 5/8 units
Efficiency of B = 1/24 units/hour
Work done by B in 10 hours = 10/25 = 5/12 units
Efficiency of C = -1/x units/hour
Work done by C in 4 hours = -4/x units
Now, According to the question:
⇒ 5/8 + 5/12 - 4/x = 1
⇒ (15x + 10x - 96)/24x = 1
⇒ x = 96.