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Question

A man wishes to cross a river in a boat. If he crosses the river in minimum time, he takes 10 minutes with a drift of 120 m. If he crosses the river taking shortest route, he takes 12.5 minutes, find the velocity of the boat with respect to water.

A
20 m/min
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B
12 m/min
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C
10 m/min
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D
8 m/min
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Solution

The correct option is A 20 m/min
Let L be the width of the river u be the speed of river and v be the speed of man w.r.t water.
For shortest time path, t=10=Lv...(i)
For shortest distance path,



t=12.5=Lv2u2=Lv1u2/v2...(ii)

Give Drift =120 m in 12 min. So, river velocity u=12012=10 m/min

Dividing (i) by (ii),
1012.5=Lv×v1u2/v2L
45=1122v2
1625=1122v2
122v2=11625=925
12v=35
v=12×53=20 m/min

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