# BOATS AND STREAMS

## About the topic boats and streams

Boats and streams play a major role quantitative aptitude test. There is no competitive exam without the questions from this topic. We have already learned this topic in our lower classes.Even though we have been already taught this topic in our lower classes, we need to learn some more short cuts which are being used to solve the problems in the above topic.

The only thing we have to do is, we need to apply the appropriate short cut and solve the problems in a limited time. This limited time will be one minute or less than one minute in most of the competitive exams.

Points to remember

 1. The direction along the stream in water is called downstream. 2. The direction against the stream in water is called upstream. 3. When the speed of a boat in still water is "a" miles/hr and the speed of the stream is "b" miles/hr, Speed downstream = (a+b) miles/hr Speed upstream = (a-b) miles/hr 4. When the speed downstream is "u" miles/hr and the speed upstream stream is "v" miles/hr, Speed in still water = 1/2(u+v)miles/hr Rate of stream = 1/2(u-v) miles/hr 5. Meaning: Speed of the boat in still water = Actual speed of the boat

## Why do students have to study this topic?

Students who are preparing to improve their aptitude skills and those who are preparing for this type of competitive test must prepare this topic in order to have better score. Because, today there is no competitive exam without questions from the topic time and work problems. Whether a person is going to write placement exam to get placed or a students is going to write a competitive exam in order to get admission in university, they must be prepared to solve  problems on boats and streams. This is the reason for why people must study this topic.

## Benefit of studying this topic

As we mentioned in the above paragraph, a person who wants to get placed in a company and a students who wants to get admission in university for higher studies must write competitive exams like placement test and entrance exam. To meet the above requirement, it is very important to score more marks in the above mentioned competitive exams. To score more marks, they have to prepare this topic. Preparing this topic would definitely improve their marks in the above exams. Preparing this topic is not difficult task. We are just going to remember the stuff that we have already learned in our lower classes

## How can students do            problems on boats and streams?

Students have to learn few basic operations in this topic and some additional tricks. Already we are much clear with the four basic operations which we often use in math. They are addition, subtraction, multiplication and division. Even though we are much clear with these four basic operations, we have to be knowing some more stuff to do the problems which are being asked from this topic in competitive exams. The stuff which I have mentioned above is nothing but the tricks and shortcuts which need to solve the problems in a very short time.

## Shortcuts we use to solve the problems

Short cut is nothing but the easiest way to solve problems related to boats and streams. In competitive exams, we will have very limited time to solve each problem. Then only we will be able to attend all the questions. If we do problems in competitive exams in perfect manner with all the steps, it will definitely take much time and we may not able to attend the other questions. So we need some other way in which the problems can be solved in a very short time. The way we need to solve the problem quickly is called as shortcut.

Here, we are going to have some problems on Time and Work . You can check your answer online and see step by step solution.

1. A man can row 18kmph in still water. It takes him thrice as long as to row up as to row down the river. Find the rate of stream (in kmph).

 (A) 6                                (B) 7 (C) 8                                (D) 9

jQuery UI Dialog functionality
Let "x" be the speed upstream. Then the speed downstream = 3x

Rate in still water = 1/2(3x+x)= 2xkm/hr
Therefore 2x = 18
x = 9
Speed upstream = 9 km/hr
Speed downstream = 3X9 = 27 km/hr

rate of the stream = 1/2(27-9) = 9 km/hr

2. A boat takes 19 hours for traveling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?

 (A) 160 km                    (B) 180 km (C) 200 km                    (D) 220 km

jQuery UI Dialog functionality
From the given information, we have
Speed downstream = (14+4) = 18 kmph
Speed upstream = (14-4) = 10 kmph

Let "x" be the distance between A and B
x/18 + (x/2)/10 =19 (Hint: Time = Distance/Speed)
x/18 + x/20 =19
(10x + 9x)/180 = 19 (L.C.M of 18,20 is 180)
19x/180 = 19
x = 180

Hence the distance between A and B is 180 km.

3. A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km down stream in 6.5 hours. The velocity of the current is

 (A) 2 kmph                    (B) 3 kmph (C) 4 kmph                    (D) 5 kmph

jQuery UI Dialog functionality
Let "x" and "y" be speed upstream and downstream respectively
From the given information, we have
24/x + 36/y = 6 ------(1)
36/x + 24/y = 13/2 ------(2)

Adding (1) and (2), we get
60/x + 60/y = 25/2 ===> 60(1/x+1/y) = 25/2
1/x + 1/y = 5/24 ------(3)

Subtracting (1) from (2), we get
12/x - 12/y = 1/2 ===>12(1/x-1/y) = 1/2
1/x - 1/y = 1/24 ------(4)

Adding (3) and (4), we get 2/x = 6/24 ===> x = 8

(3)===> 1/8 + 1/y = 5/24 ===> 1/y = (5/24)-(1/8)
1/y = 1/12 ===> y = 12

velocity of the current = 1/2(y-x) ===> 1/2(12-8)
=1/2(4) = 2 kmph

Hence the velocity of the current is 2 km/hr.

4. At his usual rowing rate Michael can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24 miles round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?

 (A)12⁄3 mph                           (B)22⁄3 mph (C)31⁄3 mph                           (D)51⁄3 mph

jQuery UI Dialog functionality
Let "x" mph be speed in still water and "y" mph be speed of the current.

Then, speed downstream = (x+y) mph
12/(x-y) - 12(x+y) = 6
By simplification, we get
x2 = y2+4y ----(1)

If the speed is doubled, speed in still water = 2x and speed of the current is same "y".
Speed down stream = (2x+y) mph and speed up stream = (2x-y) mph
12/(2x-y) - 12(2x+y) = 1
By simplification, we get
x2 = (24y+y2)/4 ----(2)
Solving (1) and (2), we get y = 8/3 = 223 mph

Hence speed of the current = 223 mph

5. The speed of a boat in still water is 10 kmph. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the current is

 (A) 6 kmph                   (B) 5 kmph (C) 4 kmph                   (D) 3 kmph

jQuery UI Accordion - Default functionality
Let "x" be the speed of the current

Speed upstream = (10-x) kmph
Speed downstream = (10+x) kmph

From the given information, we have

26/(10+x) = 14/(10-x)
26(10-x) = 14(10+x)
260-26x = 140+14x
40x = 120
x = 120/40 = 3 kmhr

Hence the speed of the current is 3 kmph
Hence the batsman's average after 17th inning is 39.