Boats and Streams
- A man rows upstream 36 km and downstream 48 km taking 6 hours each time. The speed of the current is
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As per the given in above question , we have
Rate downstream of boat = 48 = 8 kmph 6 Rate upstream = 36 = 6 kmph 6 ∴ Speed of current = 1 (Rate down stream – rate upstream) 2 Speed of current = 1 (8 – 6) = 1 kmph 2
We can find the required answer with the help of given formula :Here, p = 48 = 8 kmph 6 q = 36 = 6 kmph 6
Correct Option: C
As per the given in above question , we have
Rate downstream of boat = 48 = 8 kmph 6 Rate upstream = 36 = 6 kmph 6 ∴ Speed of current = 1 (Rate down stream – rate upstream) 2 Speed of current = 1 (8 – 6) = 1 kmph 2
We can find the required answer with the help of given formula :Here, p = 48 = 8 kmph 6 q = 36 = 6 kmph 6 Speed of Current = 1 (p - q) 2 Speed of Current = 1 (8 - 6) = 1 kmph 2
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The rate at which he rows in still water isA man rows down a river 15 km in 3 hrs. with the stream and returns in 7 1 hrs, 2
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Let speed of person in still water = p kmph and speed of current = q kmph
∴ p + q = 15 = 5 kmph ........( 1 ) 3 & p – q = 15 15 2
p - q = 2 kmph ......( 2 )
On adding equations ( 1 ) and ( 2 ) ,2p = 7 ⇒ p = 7 = 3.5 kmph 2
We can find the required answer with the help of given formula : :Here, p = 15 = 5 kmph 3 q = 15 15 2
q = 2 km/hr
Correct Option: C
Let speed of person in still water = p kmph and speed of current = q kmph
∴ p + q = 15 = 5 kmph ........( 1 ) 3 & p – q = 15 15 2
p - q = 2 kmph ......( 2 )
On adding equations ( 1 ) and ( 2 ) ,2p = 7 ⇒ p = 7 = 3.5 kmph 2
We can find the required answer with the help of given formula : :Here, p = 15 = 5 kmph 3 q = 15 15 2
q = 2 km/hrSpeed of Boat = 1 (p + q) 2 Speed of Boat = 1 (5 + 2) = 3.5 kmph 2
- A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is
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Suppose Speed of boat in still water = p kmph
Speed of current = q kmph
Rate downstream = (p + q) kmph
Rate upstream = (p – q) kmph
Distance = Speed × Time
∴ (p – q) × 2t = (p + q) × t
⇒ 2p – 2q = p + q
⇒ 2p – q = 2q + q
⇒ p = 3qCorrect Option: D
Suppose Speed of boat in still water = p kmph
Speed of current = q kmph
Rate downstream = (p + q) kmph
Rate upstream = (p – q) kmph
Distance = Speed × Time
∴ (p – q) × 2t = (p + q) × t
⇒ 2p – 2q = p + q
⇒ 2p – q = 2q + q
⇒ p = 3q⇒ p = 3 = 3 : 1 q 1
- The speed of a stream is 3 km/ hr. and the speed of a man in still water is 5 km/hr. The time taken by the man to swim 26 km downstream is :
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Given in question , Speed of a stream is 3 km/ hr and the speed of a man in still water = 5 km/hr
Time = Distance Rate downstream
Rate downstream = 5 + 3 = 8 kmph
Correct Option: B
Given in question , Speed of a stream is 3 km/ hr and the speed of a man in still water = 5 km/hr
Time = Distance Rate downstream
Rate downstream = 5 + 3 = 8 kmphTime = 26 = 13 = = 3 1 hours 8 4 4
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. Its rowing speed in still water is (in km/ hr).A man rows 750 m in 600 seconds against the stream and returns in
71 minutes 2
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According to question ,
Rate downstream = 
750 
m/minute 15 2
Rate downstream = 100 m/minuteRate downstream = 100 × 60 kmph = 60kmph 1000 Rate upstream = 750 × 18 kmph 600 5
Rate upstream = 4.5 kmph∴ Rowing speed in still water = 1 (6 + 4.5) = 10.5 = 5.25 kmph 2 2
Second method to solve this question :Here, p = 750m 15 min 2 p = 750 × 2 × 60 = 6km/hr 1000 × 15 q = 750 m = 750 × 3600 600s 1000 × 600
q = 4.5 km/hr
Correct Option: D
According to question ,
Rate downstream = 750 m/minute 15 2
Rate downstream = 100 m/minuteRate downstream = 100 × 60 kmph = 60kmph 1000 Rate upstream = 750 × 18 kmph 600 5
Rate upstream = 4.5 kmph∴ Rowing speed in still water = 1 (6 + 4.5) = 10.5 = 5.25 kmph 2 2
Second method to solve this question :Here, p = 750m 15 min 2 p = 750 × 2 × 60 = 6km/hr 1000 × 15 q = 750 m = 750 × 3600 600s 1000 × 600
q = 4.5 km/hr∴ Speed of Boat = 1 (p + q) 2 Speed of Boat = 1 (6 + 4.5) = 5.25 km/hr 2
