| Three pipes A, B and C can fill a tank separately in 8 h, 10 h and 20 h, respectively. Find the time taken by all the three pipes to fill tank when the pipes are opened together. |
A) \[5\frac{7}{11}h\]
B) \[4\frac{7}{11}h\]
C) \[8\frac{7}{11}h\]
D) \[3\frac{7}{11}h\]
E) None of these
Correct Answer: D
Solution :
| Part filled by A in \[1\,\,h=\frac{1}{8}\] |
| Part filled by B in \[1\,\,h=\frac{1}{10}\] |
| Part filled by C in \[1\,\,h=\frac{1}{20}\] |
| Part filled by (A + B + C) in 1 h |
| \[=\frac{1}{8}+\frac{1}{10}+\frac{1}{20}=\frac{5+4+2}{40}=\frac{11}{40}h\] |
| \[\therefore \]Required time to fill the tank \[=\frac{40}{11}h=3\frac{7}{11}h\] |
| Alternative method |
| Here, \[m=8,\]\[n=10\]and \[p=20\] |
| \[\therefore \]Required time to fill the tank |
| \[=\frac{mp}{mn+np+mp}\] |
| \[=\frac{8\times 10\times 20}{8\times 10+10\times 20+8\times 20}\] |
| \[=\frac{1600}{80+200+160}=\frac{1600}{440}\] |
| \[=\frac{40}{11}=3\frac{7}{11}h\] |
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