A) 6 : 15 pm
B) 7 : 12 pm
C) 8 : 23 pm
D) 8 : 35 pm
Correct Answer: B
Solution :
Pipe A is opened at 3 pm, pipe B at 4 pm and the pipe C at 5 pm |
Part of the tank filled by pipe A in 2 h \[=\frac{2}{3}\] |
Part of the tank filled by pipe B in 1 h \[=\frac{1}{4}\] |
Part of the tank filled till 5 pm \[=\frac{2}{3}+\frac{1}{4}=\frac{8+3}{12}=\frac{11}{12}\] |
Remaining part \[=1-\frac{11}{12}=\frac{1}{12}\] |
Net part emptied when A, B and C are opened |
\[=\frac{1}{3}+\frac{1}{4}-1=\frac{4+3-12}{12}=\frac{-\,\,5}{12}\] |
\[\therefore \]\[\frac{5}{12}\]Part is emptied in 1 h |
\[\therefore \]\[\frac{11}{12}\]is emptied m\[=\frac{12}{5}\times \frac{11}{12}=\frac{11}{5}\]h=2h 12 min |
Hence, the tank will be emptied at 7 : 12 pm. |
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