A) 6 Minutes
B) \[6\frac{2}{3}\] Minutes
C) \[6\frac{3}{7}\] Minutes
D) \[3\frac{1}{2}\] Minutes
Correct Answer: C
Solution :
[c] Part of the cistern filled by first pipe in 1 minute \[=\frac{1}{6}\] Part of the cistern filled by second pipe in 2 minutes \[=\frac{1}{7}\] Part of the cistern filled in first 2 minutes \[=\frac{1}{6}+\frac{1}{7}=\frac{13}{42}\] Part of cistern filled in 6 minutes \[=\frac{3\times 13}{42}=\frac{39}{42}\] Remaining part \[=1-\frac{39}{42}=\frac{3}{42}=\frac{1}{14}\] \[\therefore \] Time taken to fill \[\frac{1}{14}\]parts \[=\frac{6}{14}=\frac{3}{7}\] \[\therefore \] Total time \[=6+\frac{3}{7}=6\frac{3}{7}minutes\]
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