Pipe A and B can fill a tank in 16 hours and 24 hours , respectively and pipe C alone can empty the full tank in x hours. All the pipe were opened together At 10:30 a.m., But C was closed at 2:30 p.m. If the tank was full at 8:30 pm on the same day, then what is the value of x?

Pipe A fills at 1/16 tank per hour, B at 1/24 tank per hour. Combined fill rate = 7/96 tank per hour. All three pipes open for 4 hours (10:30 AM to 2:30 PM), then only A and B for 6 hours (2:30 PM to 8:30 PM). In 4 hours with all three: (7/96 - 1/x) × 4. In 6 hours with only A and B: (7/96) × 6 = 7/16. Total: (7/96 - 1/x) × 4 + 7/16 = 1. Solving gives x = 96 hours.