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Pipe A takes 36 hours to fill the tank and pipe B takes 12 hours. Pipe C takes 72 hours to empty the tank. If all the three pipes are opened, how much time will the tank take to be filled?1). \(10\frac{2}{7}\) hours2). \(8\frac{5}{7}\) hours3). \(9\frac{2}{7}\) hours4). \(6\frac{5}{7}\) hours |
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Answer» ⇒ Part of the tank pipe A FILLS in one minute $(= \frac{1}{{36}})$ ⇒ Part of the tank pipe B fills in one minute $(= \frac{1}{{12}})$ ⇒ Part of the tank pipe A and B fill in one minute $(= \frac{1}{{36}} + \frac{1}{{12}} = \frac{1}{9})$ ⇒ Part of the tank pipe C EMPTIES in one minute $(= \frac{1}{{72}})$ The RATE of filling is more than the rate of emptying ⇒ NET part of the tank filled in one minute = $(\frac{1}{9} - \frac{1}{{72}} = \frac{7}{{72}})$ ∴ Time taken to fill the tank is $(\frac{{72}}{7} = 10\frac{2}{7})$ hours |
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