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Boats and Streams- Important Formulae, Tricks and Shortcuts [Quantitative Aptitude]

Here are important formulas and shortcuts to solve problems on Boats and Streams. Basic knowledge regarding solving questions and problem on Boats and Streams is important for various competitive exams like IBPS, SBI Bank PO, assistant, SSC exams, Railway exam, UPSC exams.

Boats and Streams- Important Formulae, Tricks and Shortcuts



Important Formulae and Shortcuts on Boats and Stream


Speed of stream = V km/hr


Speed of boat in still water = U km/hr


When boat is moving in stream:


Direction of boat moving along stream is called downstream

  • Speed of boat downstream = (U + V) km/hr


Direction of boat moving against stream is called upstream

  • Speed of boat upstream = (U - V) km/hr


If speed of boat downstream is S1 and upstream is S2

  • Speed of boat in still water = U = (S1 + S2)/2 km/hr

  • Speed of stream = V =  (S1 - S2)/2 km/hr


Below are some examples and problem solving tricks regarding Boats and Streams


Example 1: A boat is moving downstream in a stream running at 5 km/hr. If the speed of boat in still water is 25 km/hr, find the time taken (in minutes) by boat to travel 5 km.
Soln:  Given: U = 25 km/hr, V = 5 km/hr, Distance = 5 km
Speed of boat in downstream = U + V = 25 + 5 = 30 km/hr
Time = Distance / Speed = 5/30 hr = (1/6) * 60 minutes = 10 minutes.

Example 2: A boat is moving upstream in a stream running at 5 km/hr. If the speed of boat in still water is 25 km/hr, find the distance traveled by boat in 30 minutes.
Soln: Given: U = 25 km/hr, V = 5 km/hr, Time = 30 minutes = 1/2 hr
Speed of boat in upstream = U - V = 25 - 5 = 20 km/hr
Distance = Speed * Time = 20 * (1/2) = 10 km.

Example 3: If speed of a boat upstream is 25 km/hr and downstream is 15 km/hr. Find the speed of the stream and speed of boat in still water.
Soln: Given: S1 = 25, S2 = 15
Speed of boat in still water = U = (25 + 15)/2 = 20km/hr
Speed of stream = V = (25 - 15)/2 = 5 km/hr

Example 4: In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.
Soln: Let the speed of motorboat in still wter = U
Speed of motorboat downstream = (U + 2) kmph
Time taken to travel 6 km = T1 = 6/(U + 2)
Speed of motorboat upstream = (U - 2) kmph
Time taken to trave 6 km = T2 = 6 / (U -2)
T1 + T2 = 33/60
=> 6 / (U + 2) + 6 / (U - 2) = 33/60
=> (U - 22)(11U + 2) = 0
=> U = 22                        ( We will ignore U = -2/11 as speed could not be negative)

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