Topics

A) 12 |

B) 14 |

C) 16 |

D) 18 |

Correct Answer:

B) 14 |

Description for Correct answer:

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

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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