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# Three pipes A, B and C can till a cistern 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 cistern is :

 A) 12 B) 14 C) 16 D) 18

 B) 14

Part of the tank filled by three pipes (A + B + C) in 1 hour = $$\Large \frac{1}{6}$$

$$\Large \therefore$$ Part filled by in 2 hour = $$\Large \frac{2}{6} = \frac{1}{3}$$

$$\Large \therefore$$ Remaining part = $$\Large 1 - \frac{1}{3} = \frac{2}{3}$$

Part filled by (A + B) in 7 hours = $$\Large \frac{2}{3}$$

$$\Large \therefore$$ (A + B )'s 1 hour's work = $$\Large \frac{2}{21}$$

$$\Large \therefore$$ Part filled by C in 1 hour

= Part filled by (A + B + C) in 1 hour - Part filled by (A + B) in 1 hour

= $$\Large \frac{1}{6} - \frac{2}{21} = \frac{14 - 8}{84} = \frac{6}{84} = \frac{1}{14}$$

$$\Large \therefore$$ C alone can fill the tank in 14 hours

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