Discussion
Pipes A and B can fill a tank in 8 hours and 10 hours, respectively. Both pipes were opened together for 3 hours, then B is closed and pipe C (filling pipe) is opened instantly. A and C together filled the remaining part of the tank in 39 minutes. Pipe C alone can fill the whole tank in (in hours)
Answer: C
Pipe C alone fills the tank in 2 2/3 hours. In 3 hours A and B together fill \[3\left(\frac{1}{8} + \frac{1}{10}\right)\] \[= \frac{27}{40}\] of the tank, leaving 13/40. A and C together fill this in 39 minutes, which is 13/20 hour, so their combined rate is \[\frac{13/40}{13/20} = \frac{1}{2}\] tank per hour. Then C's rate is \[\frac{1}{2} - \frac{1}{8} = \frac{3}{8}\] and C alone takes 8/3 = 2 2/3 hours. The options 3, 3 1/2 and 4 1/2 give rates of 1/3, 2/7 and 2/9 for C, which do not fit.
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