| Pipe A and B can fill a tank in 10 h and 8 h, respectively. After certain time, pipe A was closed. It took a total of 6 hours to fill the tank completely. For how many hours did pipe A work? |
A) \[4\frac{1}{4}h\]
B) \[2\frac{1}{2}h\]
C) \[1\frac{1}{9}h\]
D) \[5\frac{1}{3}h\]
Correct Answer: C
Solution :
| Part filled by pipe A is \[1\,\,h=\frac{1}{10}\] |
| Part filled by pipe B is \[1\,\,h=\frac{1}{8}\] |
| Part filled by pipe B in \[6\,\,h=\frac{6}{8}=\frac{3}{4}\] |
| Remaining part \[=1-\frac{3}{4}=\frac{1}{4}\] |
| Remaining part filled by (A + B) in 1 h |
| \[=\frac{1}{10}+\frac{1}{8}=\frac{4+5}{40}=\frac{9}{40}\] |
| Time taken to fill \[\frac{1}{4}\]part by both A and 6 |
| \[=\frac{40}{9}\times \frac{1}{4}=\frac{10}{9}h=1\frac{1}{9}h\] |
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