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A) \( \Large 3 \frac{1}{2} \ hours \) |

B) \( \Large 3 \frac{1}{4} \ hours \) |

C) \( \Large 4 \frac{1}{4} \ hours \) |

D) 4 hours |

Correct Answer:

A) \( \Large 3 \frac{1}{2} \ hours \) |

Description for Correct answer:

Let the speed of boat in still water he x kmph and that of current by y kmph.

According to the question,

\( \Large \therefore \frac{d}{x + y} + \frac{d}{x - y} = \frac{21}{4} \) ... (i)

and, \( \Large \frac{2d}{x - y} = 7 => \frac{d}{x - y} = \frac{7}{2} \) ...(ii)

By equation (ii) - (i),

\( \Large \frac{d}{x + y} = \frac{21}{4} - \frac{7}{2} = \frac{21 - 14}{4} = \frac{7}{4} \)

=> \( \Large \frac{2d}{x + y} = \frac{7}{2} = 3 \frac{1}{2} hours \)

Let the speed of boat in still water he x kmph and that of current by y kmph.

According to the question,

\( \Large \therefore \frac{d}{x + y} + \frac{d}{x - y} = \frac{21}{4} \) ... (i)

and, \( \Large \frac{2d}{x - y} = 7 => \frac{d}{x - y} = \frac{7}{2} \) ...(ii)

By equation (ii) - (i),

\( \Large \frac{d}{x + y} = \frac{21}{4} - \frac{7}{2} = \frac{21 - 14}{4} = \frac{7}{4} \)

=> \( \Large \frac{2d}{x + y} = \frac{7}{2} = 3 \frac{1}{2} hours \)

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