If the ratio of speed of upstream and down stream is $3 : 4$ , then the ratio of the speed of boat in still water and the speed of the stream is

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$2 : 14$

$14 : 2$

$7 : 1$

$1 : 7$

answer is B, D.

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Detailed Solution

Let speed of boat in still water be $' x' k m p h$

$∴$ let speed of stream be $' y' k m p h$

Speed of boat up stream $= (x - y) k m p h$

Speed of boat down stream $= (x + y) k m p h$

Given ratio of speed of boat up stream and down stream $= 3 : 4$

$∴$ $\frac{x - y}{x + y} = \frac{3}{4}$

$4 (x - y) = 3 (x + y)$

$4 x - 4 y = 3 x + 3 y$

$4 x - 3 x = 3 y + 4 y$

$1 x = 7 y$

$\frac{x}{y} = \frac{7}{1}$

$∴$ $x : y = 7 : 1$

Ratio of speed of boat in still water and speed of the stream $= 7 : 1$

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