Boats and Streams Formula  Problem Solving Shortcut Tricks, Solved Questions
Boats and Streams
Boats and Streams chapter is one of the important topics
in quantitative aptitude questions. So many students have problem in this topic;
some students think that this topic is extremely time consuming but from now do
not worry about that because we are providing you Boats and stream formula and
problem solving shortcut tricks. These tricks and solved questions will be
useful in your preparation of competitive government exams.
Boats and streams topic covers minimum 23 questions in every exam and Aptitude questions on this topic are common in most of the aptitude tests for companies like Infosys, TCS, and HCL etc. The benefit with questions on boats and streams are that there are only two fundamental concepts following them, and students can solve several questions with these concepts. In this article we are giving you some tricks, how to solve boats and streams problems simply and rapidly.
Boats and Streams
Problem Solving Shortcut Tricks
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?
Solution: Let speed of boat in still water is b km/hr and speed of stream is s km/hr.
Then b + s = d and b – s = u
Solving the 2 equations we get,
b = (d + u)/2
s = (d – u)/2
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?
Solution: 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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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 * [(b^{2}  s^{2}) / 2b]
OR
Short trick: d = [t * (Speed to go downstream) * (Speed
to go upstream)]/[2 * Speed of boat or man in still water]
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
Solution: Time taken to go upstream = t + Time taken to go downstream
(d / (b  s)) = t + (d / (b + s))
=> d [ 2s / (b^{2}  s^{2} ] = t
So, d = t * [(b^{2}  s^{2}) / 2s]
OR
Short trick: d = [t * (Speed to go downstream) * (Speed
to go upstream)] / [2 * Speed of still water]
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Techniques to Double Your Score
If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,
If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,
Speed of boat downstream = (x + y) km/h
Important Points of Boats and Streams Formula
When speed of boat
is given then it means speed in the still water, unless it is stated otherwise.
Some Basic Formulas
Speed of boat in still water is
= ½ (Downstream Speed + Upstream Speed)
Speed of stream is
= ½ (Downstream Speed – Upstream Speed)
Take a Test Now

Boats and streams formulas
Short tricks with formula for boats and streams is given as
you expected,
Downstream / Upstream:
Direction along the stream is called Downstream.
Direction against the stream is called upstream.
If the speed in the still
water is x km / hr and the speed of the stream is y km / hr then,
 Speed downstream = (x + y) km / hr.
 Speed upstream = (x – y) km / hr.
If the speed downstream is u
km / hr and the speed upstream is v km / hr then,
 Speed in still water = (1 / 2) (a + b) km / hr.
 Rate of stream = (1 / 2) (a – b) km / hr.
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Some Important Solved Questions:
Types of Questions
asked in Previous Exam by SSC
Type 1: When
the distance covered by boat in downstream is same as the distance covered by
boat upstream. The speed of boat in still water is x and speed of stream
is y then ratio of time taken in going upstream and downstream is,
Short Trick:
Time taken in upstream: Time taken in Downstream = (x+y)/(xy)
1) A man can row
a boat @ 9 km ph in still water. He takes double the time to move upstream than
to move the downstream – the same distance. Find the speed of the stream?
According to Question and formula given above:
Let the downward time = 1 hour and
so the upward time = 2 hours.
1/9+s = 2/9s (Since distance is the same)
18 + 2 s = 9 – s (By cross
multiplication)
18 – 9 = s + 2 s
9 = 3 s
Hence s or Speed of stream = 9/3 = 3 km ph Answer.
OR
Simply
b + s = 2(b –s)
b + s = 2b – 2s
s + 2s = 2b –b
OR
b = 3s or 9 = 3s (b = 9 is given) =
3 km ph Answer
2) A boat runs at
20 km ph along the stream and 10 km ph against the stream. Find the ratio of
speed of the boat in still water to that of the speed of the stream?
ATQ (According to Question) and formula given above:
Speed of Boat = ½ (20 + 10) = 15 km ph.
Speed of Stream = ½ (20 – 10) = 5 km
ph.
Ratio: 15:5 = 3:1
Answer.
3) Find the speed
of the stream when a boat takes 5 hours to travel 60 kms downstream at a rate
of 10 kms per hour in still water?
According to
Question and formula given above:
Speed b + s =
60/5 = 12 km ph
Speed b = 10 km ph
So speed is = 1210 = 2
km ph Answer.
4) If a man rows
6 km downstream in 3 hours and 2 km upstream in 2 hours then how long will he
take to cover 9 kms in stationary (still) water?
According to Question and formula given above:
Speed of Boat in
still waters = ½ (6/3 + 2/2) = ½ (2 + 1) = 1.5 km ph
Time taken for 9
kms = 9/1.5 = 6 hours Answer
5) A boat covers
a certain distance in one hour downstream with the speed of 10 km ph in still
water and the speed of current is 4 km ph. Then find out the distance travelled?
According to Question and formula given above:
Distance = Speed
x Time = 1 x (10+4) = 14 kms.
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