A) 12 km/hr, 3 km/hr | B) 9 km/hr, 3 km/hr |

C) 8 km/hr, 2 km/hr | D) 9 km/hr, 6 km/hr |

Explanation:

Let the speed of the boat = p kmph

Let the speed of the river flow = q kmph

From the given data,

$\mathbf{2}\mathbf{}\mathbf{x}\mathbf{}\frac{\mathbf{28}}{\mathbf{p}\mathbf{}\mathbf{+}\mathbf{}\mathbf{q}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{28}}{\mathbf{p}\mathbf{}\mathbf{-}\mathbf{}\mathbf{q}}$

=> 56p - 56q -28p - 28q = 0

=> 28p = 84q

=> p = 3q.

Now, given that if

$\frac{\mathbf{28}}{\mathbf{3}\mathbf{q}\mathbf{}\mathbf{+}\mathbf{}\mathbf{2}\mathbf{q}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{28}}{\mathbf{3}\mathbf{q}\mathbf{}\mathbf{-}\mathbf{}\mathbf{2}\mathbf{q}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{672}}{\mathbf{60}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{28}{5\mathrm{q}}+\frac{28}{\mathrm{q}}=\frac{672}{60}\phantom{\rule{0ex}{0ex}}\mathbf{=}\mathbf{}\mathbf{}\mathbf{q}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}\mathbf{}\mathbf{kmph}\phantom{\rule{0ex}{0ex}}\mathbf{=}\mathbf{}\mathbf{}\mathbf{x}\mathbf{}\mathbf{}\mathbf{=}\mathbf{3}\mathbf{q}\mathbf{}\mathbf{=}\mathbf{}\mathbf{9}\mathbf{}\mathbf{kmph}$

Hence, **the speed of the boat = p kmph = 9 kmph and the speed of the river flow = q kmph = 3 kmph.**

A) 2(2 + √17) | B) 3(2 + √17) |

C) 2(4 + √15) | D) 3(4 + √17) |

A) 0.20 Hz | B) 625 Hz |

C) 250 Hz | D) 100 Hz |