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Question
Choose the most appropriate option
A man rows to a place 45 k.ms distant and back in 12 hours. He realises that he can row 5 k.ms downstream at the same time as 3 k.ms against the stream. The velocity of the stream is:
Options
4 k.ms/hr
1.5 k.ms/hr
1 k.m/hr
2 k.ms/hr
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Solution
2 k.ms/hr
Explanation:
Suppose that he moves 5 km downstream in x hours
Then, Speed downstream`="distance"/"Time"`
`=5/"x"` km/hr
Here, he can row 5 km with the stream at the same time as 3 km against the stream
i.e. Speed upstream`=3/5` of speed downstream
Speed upstream`=3/"x"` km/hr
He rows to a place 45 km distant and comes back in 12 hours.
`⇒41/((5/"x"))45/((3/"x"))=12`
⇒ 9x + 15x = 12
⇒ 3x + 5x = 4
⇒ 8x = 6
∴`"x"=4//8=1//2`
Hence. Speed downstream `5/"x"=5/((1/2))` = 10 km / hr
Speed upstream`=3/"x"=3/((1/2))` = 6 km/hr
∴ Ratio of stream`=1/2(10-6)`
`=1/2xx4`= 2 km/hr
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