| There are 7 pipes attached with a tank out of which some are inlets and some are outlets. Every inlet can fill the tank in 10 h and every outlet can empty the tank in 15 h. When all the pipes are opened simultaneously, the tank is filled up in \[2\frac{8}{11}h.\]Find the numbers of inlets and outlets. |
A) 5, 2
B) 6, 1
C) 4, 3
D) 3, 4
E) None of these
Correct Answer: A
Solution :
| Let number of outlets be x. |
| \[\therefore \]Number of inlets \[=(7-x)\] |
| Time taken to fill the tank when all the pipes are opened \[=\frac{30}{11}h\] |
| Part of tank filled in 1 h when all the pipes are opened \[=\frac{11}{30}h\] |
| According to the question, |
| \[\frac{7-x}{10}-\frac{x}{15}=\frac{11}{30}\] |
| \[\Rightarrow \]\[\frac{3\,\,(7-x)-2x}{30}=\frac{11}{30}\] |
| \[\Rightarrow \]\[21-3x-2x=11\]\[\Rightarrow \]\[5x=10\] |
| \[\therefore \] \[x=2\] |
| Hence, number of outlets \[=2\] |
| and number of inlets \[=7-2=5\] |
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