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A) 3 kmph |

B) 2 kmph |

C) 2.5 kmph |

D) 4 kmph |

Correct Answer:

A) 3 kmph |

Description for Correct answer:

Speed of current = x kmph

\( \Large \therefore \) Rate downstream

= (6 + x) kmph

Rate upstream = (6 - x) kmph

\( \Large \therefore \frac{36}{6 - x} - \frac{36}{6 + x} = 8 \)

=> \( \Large 36(\frac{6 + x - 6 + x}{(6 - x)(6 + x)}) = 8 \)

=> \( \Large \frac{36 \times 2x}{(6 - x)(6 + x)} = 8 \)

=> \( \Large 9x = 36 - x^{2} \)

=> \( \Large x^{2} + 9x - 36 = 0 \)

=> \( \Large x^{2} + 12x - 3x - 36 = 0 \)

=> \( \Large x(x + 12) - 3(x + 12) = 0 \)

=> \( \Large (x - 3) (x + 12) = 0 \)

=> x = 3 kmph

Speed of current = x kmph

\( \Large \therefore \) Rate downstream

= (6 + x) kmph

Rate upstream = (6 - x) kmph

\( \Large \therefore \frac{36}{6 - x} - \frac{36}{6 + x} = 8 \)

=> \( \Large 36(\frac{6 + x - 6 + x}{(6 - x)(6 + x)}) = 8 \)

=> \( \Large \frac{36 \times 2x}{(6 - x)(6 + x)} = 8 \)

=> \( \Large 9x = 36 - x^{2} \)

=> \( \Large x^{2} + 9x - 36 = 0 \)

=> \( \Large x^{2} + 12x - 3x - 36 = 0 \)

=> \( \Large x(x + 12) - 3(x + 12) = 0 \)

=> \( \Large (x - 3) (x + 12) = 0 \)

=> x = 3 kmph

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