Boats and Streams Formula
All the students who are searching the Boats and Streams
Formula they have finally reached at right place because in this article mostly
all
the types of questions are covered by the team members of the portal for
all those participants who are ready to become master in the Boats and Streams
chapter. We all know that quantitative aptitude section possess Boats and
Streams questions definitely. Applicants who don’t know the basics of the
problem solving they face problem in this topic. Here we are providing you
Boats and stream formula and problem solving shortcut tricks under one roof.
These tricks and solved questions will be useful in your preparation of
competitive government exams.
In those exams where Boats and streams topic covers it is
said that at least 2-3 questions will also be there in the Aptitude section. These
types of questions are generally asked in most of the aptitude tests for
companies like Infosys, TCS, HCL, all government job exams etc. Advantage to
ask this question on boats and streams is to search the capacity of the mind to
the appliers who are willing to appoint in a special organization. There are
only two fundamental concepts following in such questions and students can
solve several questions with these concepts. Hey guys learn all the given Shortcut
Tips & Tricks to Solving Problem from the below portion of the article. All
the best!!
Boats and Streams Formula Shortcut Tips to Solving Problem
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
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
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 / (b2 - s2 ] =
t
So, d = t * [(b2 - s2) /
2s]
OR
Short trick: d = [t * (Speed to go downstream) * (Speed
to go upstream)] / [2 * Speed of still water]
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)
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.
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)/(x-y)
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 = 2/9-s (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 = 12-10 = 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.
Reminder:
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