Boats and Streams
 The speed of boat upstream and speed of boat downstream are 7 km/h and 13 km/h, respectively. Then the speed of stream and the speed of boat in still water is ?

 10 km/h and 3 km/h
 15 km/h and 9 km/h
 20 km/h and 6 km/h
 40 km/h and 12 km/h

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Rate in still water=[(1/2)(u+v)] km/h
Rate of current=[(1/2)(uv)] km/h
where u= speed of boat in downstream
v=speed of boat in upstreamCorrect Option: A
Rate in still water=[(1/2)(u+v)] km/h
Rate of current=[(1/2)(uv)] km/h
where u= speed of boat in downstream
v=speed of boat in upstream
Speed of boat in still water=[(1/2)(7+13)] =10 km/h
Speed of the stream =[(1/2)(137)]=3 km/h
 The speed of a boat in still water is 10 km/h. If it can travel 26 km downstream and 14 km upstream in the same time , then the speed of stream is ?

 2 km/h
 2.5 km/h
 3 km/h
 None of these

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Let the speed of the stream = x km/h
∴ Speed of boat in still water = 10 km/h
Speed of boat downstream = (x + 10) km/h
Speed of boat upstream=(10  x) km/h
Correct Option: C
Let the speed of the stream = x km/h
∴Speed of boat in still water = 10 km/h
Speed of boat downstream = ( x + 10) km/h
Speed of boat upstream=(10  x) km/h
∴ Time taken to travel 26 km downstream=[ 26 / ( 10 + x ) ] h
Time taken to travel 14 km upstream=[ 14 /( 10  x )] h
⇒ By condition [ 26 / ( 10 + x)]=[ 14 / ( 10  x)]
⇒ 26(10x)=14(10+x)
⇒ 26026x =140 + 14x
⇒ 40x=120
⇒ x = 3 Here, speed of stream = 3 km/h
 A boat goes 40 km. upstream in 8 hours and 36 km. downstream in 6 hours. The speed of the boat in standing water is ?

 6.5 km.hr
 6 km/hr
 5.5 km/hr
 5 km/hr

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Speed upstream = (40/8) km/hr = 5 km/hr
Speed downstream = (36/6) km/hr = 6 km/hr
Speed of boat in still water = (5 + 6)/2 km/hr = 5.5 km/hr.Correct Option: C
Speed upstream = (40/8) km/hr = 5 km/hr
Speed downstream = (36/6) km/hr = 6 km/hr
Speed of boat in still water = (5 + 6)/2 km/hr = 5.5 km/hr.
 If a man's rate with the current is 12 km/hr and the rate of the current is 1.5 km/hr then man's rate against the current is ?

 9 km/hr
 6.75 km/hr
 5.25 km/hr
 7.5 km/hr

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Let the rate against the current be x km/hr.
Then, (12  x) / 2 = 1.5Correct Option: A
Let the rate against the current be x km/hr.
Then, (12  x) / 2 = 1.5
⇒ 12  x = 3
⇒ x = 9 km/hr
 If a man rows at 5 km/hr in still water and 3.5 km/hr against the current his rate along the current is ?

 8.5 km/hr
 6.5 km/hr
 6 km/hr
 4.25 km/hr

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Speed of current = 5  3.5 = 1.5 km/hr.
Correct Option: B
Speed of current = 5  3.5 = 1.5 km/hr.
So the speed of man along the current = 5 + 1.5 = 6.5 km/hr