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Question

A man rows a boat upstream a certain distance and then returns back to the same place. If the time taken by him in going upstream is twice the time taken in rowing downstream, find the ratio of the speed of the boat in still water and the speed of the stream.


A
2 : 1
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B
3 : 2
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C
5 : 3
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D
3 : 1
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Solution

The correct option is D 3 : 1
Let the distance$$=d$$,
The speed of the boat $$=x$$ and the speed of the water current$$=y$$.
UPSTREAM-
The relative speed of the boat & water current$$=x-y$$.
Then the time taken $$=\cfrac { d }{ x-y } $$.
DOWNSTREAM-
The relative speed of the boat & water current=x+y.
Then the time taken $$=\cfrac { d }{ x+y } $$.
So, by the given condition,
$$\cfrac { d }{ x-y } =2\times \cfrac { d }{ x+y } \\ \Longrightarrow 2x-2y=x+y\\ \Longrightarrow x=3y\\ \Longrightarrow \cfrac { x }{ y } =\cfrac { 3 }{ 1 } \\ i.e\quad x:y=3:1$$
So the required ratio $$=3 : 1$$

Mathematics

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