| A, B and C are three pipe- connected to a tank, A and B together fill the tank in 6 h, B and C together fill the tank m 10 h and A and C together fill the tank in 12 h. In how much time A, B and C fill up the tank together? |
A) \[9\,\,h\]
B) \[5\frac{3}{7}h\]
C) \[5\frac{2}{7}h\]
D) \[5\frac{5}{7}h\]
E) None of these
Correct Answer: D
Solution :
| Pan filled by (A + B) in 1 h \[=\frac{1}{6}\] |
| Part tilted by (B + C) in 1 h \[=\frac{1}{10}\] |
| Part filled by (A + C) in 1 h \[=\frac{1}{12}\] |
| \[\therefore \]Part filled by 2 (A + B + C) in 1 h |
| \[=\frac{1}{6}+\frac{1}{10}+\frac{1}{12}\] |
| \[=\frac{10+6+5}{60}=\frac{21}{60}=\frac{7}{20}\] |
| \[\therefore \]Part filled by (A + B+ C) in 1 h \[=\frac{7}{2\times 20}=\frac{7}{40}\] |
| \[\therefore \] \[=\frac{40}{7}=5\frac{5}{7}h\] |
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