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Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is (a) 10(b) 12 (c) 14 (d) 16 |
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Answer» (c) 14 Part of the tank filled by (A + B + C) in 2 hours = 2 x \(\frac{1}{6}\) = \(\frac{1}{3}\) Remaining part = 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\) \(\therefore\) \(\frac{2}{3}\)rd of the tank is filled by (A + B) in 7 hours. \(\therefore\) The whole tank is filled by (A + B) in \(\big(7\times\frac{3}{2}\big)\) hours = \(\frac{21}{2}\) hours \(\therefore\) Part of the tank filled by C in 1 hour = Part of the tank filled by (A + B + C) in 1 hour - Part of the tank filled by (A + B) in 1 hour = \(\frac{1}{6}\) - \(\frac{2}{21}\) = \(\frac{3}{42}\) = \(\frac{1}{14}\) \(\therefore\) C can fill the whole tank in 14 hours. |
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