A) 360
B) 300
C) 600
D) 900
Correct Answer: C
Solution :
[c] Part filled by first pipe in 1 hour \[=\frac{1}{10}\] Part filled by second pipe in 1 hour \[=\frac{1}{12}\] Suppose the waste pipe can empty the full tank in x hours. Then, part emptied by waste pipe in 1 hour \[=\frac{1}{x}\] All the three pipes can fill the tank in 20 hours I.e. part filled by all three pipes in hour \[=\frac{1}{20}\] Now, \[\Rightarrow \,\,\,\frac{1}{10}+\frac{1}{12}-\,\frac{1}{x}=\frac{1}{20}\] \[\Rightarrow \,\,\,\frac{1}{x}=\frac{1}{10}+\frac{1}{12}-\,\frac{1}{20}=\frac{8}{60}=\frac{2}{15}\] \[\therefore \,\,\,x=\frac{15}{2}\] i.e, the waste pipe can empty the full tank in\[\frac{15}{2}\]hour Given that the waste pipe can empty 80 gallons per hour. Therefore, in \[\frac{15}{2}\] hours, it can empty \[\frac{15}{2}\times 80=600\]gallons. .Hence, volume of the tank = 600 gallons.
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