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Question

The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. [CBSE 2017]

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Solution

Let, speed of stream be x km/h
Speed of boat = 15 km/h
Distance from each side = 30 km
We know that time taken =distance coveredSpeed
Total speed of the boat while going upstream =15-x km/h
Time taken to go upstream =3015-x hrs
Total speed of boat while going downstream =15+x km/h
Time taken to go downstream =3015+x hrs
Total time of the journey =412hrs = 4.5 hrs
3015-x+3015+x=4.530(15+x)+(15-x)(15)2-x2=4.53015+x+15-x=4.5(15)2-x23030=4.5225-x230×304.5=225-x2225-x2=200x2=25x=±5
Ignore the negative value.
So, the speed of the stream = x = 5 km/h

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