Boats and Streams - Aptitude Test Tricks, Formulas & Shortcuts

The advantage with questions on boats and streams are that there are only two basic concepts behind them, and you can solve any questions with these concepts. This article explains how to solve boats and streams problems easily and quickly. The types of questions that can be expected from quantitative aptitude section of boats and streams include following

• You will be given the speed of boat in still water and the speed of stream. You have to find the time taken by boat to go upstream and downstream.
• You will be given the speed of boat to go up & down the stream, you will be asked to find speed of boat in still water and speed of stream
• You will be given speed of boat in up and down stream and will be asked to find the average speed of boat.
• You will be given the time taken by boat to reach a place in up and downstream and will be asked to find the distance to the place

The key point here is you can solve any of these questions using the formulas and short cuts given below.

Formulas and short cuts given below are also applicable to problems involving

1. Cyclist and wind: cyclist analogous to boat and wind analogous to stream
2. Swimmer and stream:  swimmer analogous to boat

You can also try

• Tricks to crack aptitude questions on Pipes-and Cisterns
• Important formulas and Tips to solve Mixtures and Alligations aptitude questions

Basic Concepts of Questions on Boats and Streams

1. A boat is said to go downstream, if the boat goes in the direction of stream.
2. A boat is said to go upstream, if the boat goes opposite to the direction of stream.

Basic Formulas

1. If speed of boat in still water is b km/hr and speed of stream is s km/hr,
• Speed of boat in downstream = (b  + s) km/hr , since the boat goes with the stream of water.
• Speed of boat in upstream = (b  - s) km/hr. The boat goes against the stream of water and hence its speed gets reduced.

Shortcuts With Explanation

Scenario 1: Given a boat travels downstream with speed d km/hr and it travels with speed u km/hr upstream. Find the speed of stream and speed of boat in still water.

Let speed of boat in still water be bkm/hr and speed of stream be skm/hr.
Then b + s  = d and b – s = u.
Solving the 2 equations we get,
b = (d + u)/2
s = (d – u)/2

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Scenario 2: A man can row a boat, certain distance downstream in td hours and returns the same distance upstream in tu hours. If the speed of stream is s km/h, then the speed of boat in still water is given by

We know distance = speed * time
Let the speed of boat be b km/hr
Case downstream:
    d = (b + s) * td
Case upstream:
    d = (b - s) * tu

=>    (b + s) / (b - s) = tu / td

b = [(tu + td) / (tu - td)] * s

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Scenario 3: A man can row in still water at b km/h. In a stream flowing at  s km/h, if it takes him t hours to row to a place and come back, then the distance between two places, d is given by

Downstream:  Let the time taken to go downstream be td
    d = (b + s) * td

Upstream: Let the time taken to go upstream be tu
    d = (b - s) * tu

td + tu = t
[d / (b + s)] + [d / (b - s)] = t
So, d = t * [(b² - s²) / 2b]
OR 
d = [t * (Speed to go downstream) * (Speed to go upstream)]/[2 * Speed of boat or man in still water]

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Scenario 4: A man can row in still water at b km/h. In a stream flowing at s km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance d is given by

Time taken to go upstream = t + Time taken to go downstream
(d / (b - s)) = t + (d / (b + s))
=> d [ 2s / (b² - s² ] = t
So, d = t * [(b² - s²) / 2s] 
OR 
d = [t * (Speed to go downstream) * (Speed to go upstream)] / [2 * Speed of still water]