## 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 2-3 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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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]

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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)

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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 upstreamTime 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

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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.

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.