Pipes 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 pipes 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 p.m. on the sameday, then what is the value of x?

Let the total work be 48.
($$\because$$ LCM of 16, 24, x is 48x)
Efficiency of pipe A = 48x/16 = 3x
Efficiency of pipe B = 48x/24 = 2x
Efficiency of pipe C = -48x/x = -48
(- sign shows the empty pipe.)
Pipe A and B Works 10:30 a.m to 8:30 p.m.
So, time  = 8:30 p.m. - 10:30 a.m = 10 hr
Work done in 10 hr = efficiency $$\times time$$ = (3x + 2x) \times 10 = 50x
Work done by pipe C = 50x - 48x = 2x
pipe C opened at 10:30 a.m. to 2:30 p.m
So, time taken by pipe C = 2:30 p.m - 10:30 = 4 hr
Work done in 4 hr by pipe C = 2x
48 $$\times$$ 4 = 2x
x = 96