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Question

A steamer going downstream in a river, covers the distance between $$2$$ towns in $$15$$ hours. Coming back upstream, it covers this distance in $$20$$ hours. The speed of the water is $$3$$ km/hr. Find the distance between two towns.


A
360 km
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B
220 km
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C
180 km
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D
120 km
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Solution

The correct option is A $$360$$ km
Let the speed of the stream be $$x$$ km/h.
Given, speed of water $$= 3$$ km/h 
Therefore, downstream speed $$= (x + 3)$$ km/h
and upstream speed $$=(x-3)$$
 km/h
Again, time taken in downstream and upstream is $$15$$ hours and $$20$$ hours respectively.
Now, distance downstream $$=$$ distance upstream
$$\Rightarrow 15(x+3)=20(x-3)$$
$$ \Rightarrow 15x+45=20x-60$$
$$ \Rightarrow 15x-20x=-60-45$$
$$ \Rightarrow -5x=-105$$ or $$ x=21$$ km/h
Therefore, downstream speed $$= 21 + 3 = 24$$ km/h
So, distance between the two towns $$=$$ Downstream speed $$\times$$ Time taken in downstream 
$$= 24 \times 15 = 360$$ km

Physics

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