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Boats & Streams Tricks & Tips Part

Boats & Streams Tricks & Tips Part



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Terms Related To Boats And Sreams:

                  Speed of the boat:It refers to the velocity of the boat in standing water ,let it be X.

                   Speed of the Stream: It refers to the velocity at which the water flows,let it be Y.

                   Upstream Speed (U): It is expressed as the (Speed of the Boat – Speed of the Stream) =X-Y. They row the boat in  the opposite direction to the flow of the stream.

                   Downstream Speed (D): It is expressed as the (Speed of the Boat + Speed of the Stream) =X+Y. They Row along the flow of Stream.

                    Speed of the boat in still water when upstream and downstream speed is given=1/2(D+U)

All about Boats and Streams – Types and Essential Tips:

Dear Aspirants, Here we have given the important points that you have to remember while solving boats and streams problems and its types. Definitely this is will help you, make use of it.

Introduction:

  1. Still Water:If the water is not moving then it is called still water.
  2. Stream:Moving water of the river is called stream.
  3. Upstream:If a boat or a swimmer moves in the opposite direction of the stream then it is called upstream.
  4. Downstream:If a boat or a swimmer moves in the same direction of the stream then it is called downstream.

Points to remember:

  1. When speed of boat or a swimmer is given then it normally means speed in still water.
  2. If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,
  3. Speed of boat or swimmer upstream = (x − y) km/h
  4. Speed of boat or swimmer downstream = (x + y) km/h

iii.   Speed of boat or swimmer in still water = 1/2(Downstream + Upstream)

  1. Speed of stream = 1/2(Downstream – Upstream)

Types of problems:

1.A man can row certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of stream is y km/h, then the speed of man in still water is given by

= y×(t2 + t1) / (t2 – t1)

2.A man can row certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of stream is y km/h, then the speed of man instill water is given by

= y× (t2 – t1) / (t2 + t1)

3.A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes ‘t’ hours to row to a place and come back, then the distance between two places is given by

= [t× (x2 – y2)]/(2 × x)

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

= [t× (x2 – y2)]/(2×y)

5.A man can row in still water at x km/h. In a stream flowing at y km/h, if he rows the same distance up and down the stream, then his average speed is given by

= (x2 – y2)/x

6.A man can row a distance ‘D’ upstream in t1 hrs and he rows the same distance down the stream in t2 hrs then speed is given by

Stream speed = [D×(t1-t2)]/(2×t1×t2)

7.A man can row a distance ‘D’ upstream in t1 hrs. and he rows the same distance down the stream in t2 hrs. then speed is given by

Man speed = [D×(t1+t2)]/(2×t1×t2)

 

#.1 TYPE 1:

BASED ON TIME, SPEED AND DISTANCE:

  1. A boat can travel with a speed of 13km/hr in still water. If the speed of the stream is 4km/hr.Find the time taken by the boat to go 68km downstream?
Explanation:

Speed of the boat in still water(X)=13km/hr,

Speed of the stream(Y)=4km/hr.

Relative Speed of the boat in downstream=X+Y        17km/hr

                 Time=Distance/Speed

Time=68/17=4hrs

 2.A motorboat ,whose speed is 15km/hr in still water goes 30 km downstream and comes back in a total of 4hrs30mins.The speed of the stream in(km/hr)?

Explanation:

Speed of the Boat in Still Water(X)=15km/hr,

Time T=4hr 30min(for DownStream+UpStream)

Let the speed of the Stream=Y.

DownStream Speed=Speed of Boat +Speed of the Stream

=15+Y

UpStream Speed=Speed of the Boat-Speed of the Stream

=15-Y

                       Time =Distance/Speed

Time =4hr 30min=9/2hr

(9/2)=(30/(15+Y) + 30/(15-Y))

9/2=900/(225-Y^2)

Y=5

Speed of the Stream=5km/hr.

 

#.2 TYPE 2:

BASED ON RATIO:

1.A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and the  stream is?

Explanation:

Let the man’s upstream speed be X

Man’s downstream speed be 2x

Speed of the boat in still water when upstream and downstream speed is given=1/2(D+U) Speed of the stream =1/2(D-U)

Speed of the Boat Speed of the Stream
=½(2X+X)=3X/2

=3

½ (2X-X)=X/2

1

The ratio between speed of the boat to the speed of the stream=3:1

#.3 TYPE 3:

BASED ON EFFICIENCY:

1.A man can row 12km/hr in still water .He finds that it takes him thrice as much time to row up the river as it takes to row down the river.What is the  speed of the current?

Explanation:

Let the distance be D,

Speed of the boat in still water=12km/hr.

Speed of the current=Ykm/hr

Time taken during Upstream Time taken during downstream
3 1

Distance =Time *Speed

upstream=3*(12-Y){ Speed of the Boat – Speed of the Stream}

Downstream=1*(12+Y){ Speed of the Boat +Speed of the Stream}

Distance is same here

3*(12-Y)=12+Y

36-3Y=12+Y

4Y=24

Y=6km/hr

Speed of the Stream=6km/hr

# 4.TYPE 4:

SOLVING BY EQUATIONS:

1.A person can row 18km downstream and 27km upstream in three hours and 18km upstream and 27km downstream in 2hours 42minutes.What is the upstream and Downstream Speed?

Explanation:

Downstream D=X+Y  Upstream U=X-Y

Therefore,

18D+27U=3

27D+18U=27/10

Solving   above  we get U=2/25  and   D=14/300

# 5.TYPE 5:

BASED ON AVERAGES:

1.A Man can row at a speed of 5km/hr in still water to a certain distance  upstream and back to the starting point in ariver,which flows at 2km/hr.Find the average speed for the total journey?

Explanation:

Average when  2 speeds are given for travelling the same distance too and fro then the average speed =2DU/(D+U)

Where D=Speed when travelling Downstream,U=Speed when travelling Upstream.

Downstream Speed=Speed of the Boat + Speed of the Stream .D=5+2=7km/hr

Upstream Speed =Speed of the Boat – Speed of the Stream.U=5-2=3km/hr

Average Speed=2*7*3

2*7*3     42
3+7         10

4.2km/hr

 

1)A Man can row 60km Upstream & 88 km downstream in 20 hours.Also,he can row 80km upstream and 110km downstream in 26 hours.Find the rate of the current and the speed of the man in still water?

These type of Problems can be just solved by forming equation,You have to Remember only one thing that,Upstream Speed=1/x and Downstream Speed=1/y

EXPLANATION

Given that,

60U + 88D=20

80U+110D=26

Since U=1/X & D=1/Y

X=5.Y=11

Therefore,

Rate in Still Water=(Upstream Speed+DownStream Speed)/2

=(11+5)/2

=16/2

Rate in StillWater=8Km/hr

Rate of Current=(11-5)/2

=6/2

Rate Of Current=3Km/hr


2)City A and B were 600 km Apart.Meenesh live in City A & Mithesh live in City B.The River flows at the rate of 5 km/hr.Meenesh can row a boat at the rate of 25km/hr in still water at the same time Mithesh can row a boat at the rate of 15km/hr in Still water.Find at what time they meet for the first time & Second Time?

EXPLANATION

Given that,

The Cities where 600 Km Apart,

Speed of Meenesh in Still water=25km/hr

Speed of Mithesh in Still water=15km/hr

Speed of Stream=5 km/hr

SPEED OF MEENESH:

DownStream Speed=Speed of Still Water + Speed of Stream =25 + 5 =30 km/hr

UpStream Speed=Speed of Still Water -Speed of Stream=25 -5=20 km/hr

SPEED OF MITHESH:

DownStream Speed=15+5=20km/hr

UpStream Speed=15-5=10km/hr

Meenesh & Mithesh will Meet for the First Time:

Here the Distance =600kms

Relative Speed=25+15=40km/hr

Have you Remembered ,what we had written here,

To Cross Each Other when they travel in the Opposite Direction,

=Distance/Relative Speed

=600 km/Relative Speed

When they travel in Opposite Direction their Speeds should be Sum up

When they travel in Same Direction their Speeds should be Subtracted.

=600/40(Because they were travelling in Opposite Direction)

=15 hours

They will meet Each Other after 15 hours of their journey

Their Second Meet:

Meenesh would Reach City B :

Time=Distance/Speed

=600/(25+5)[Downstream Speed=Speed in Still Water+Speed of Stream]

=600/30

=20hours

Meenesh Reach City B after 20 hours

At the same time Mithesh would Reach,

Distance travelled by Mithees=Time*Speed

=20 hours*(15-5)[Because Mithesh is travelling Upstream]

=20*10=200 km

Now,Friends When Meenesh in City B,Mithesh is 200 km ahead of City B.

What is the distance between them,

=200Km,

Speed of Meenesh =25-5=20km/hr(Upstream Speed=Speed in Still Water-Speed of Stream)

Speed of Mithesh=15-5=10km/hr

Relative Speed=200/(20-10)

=200/10

=20hours

They will meet for the Second time at 20+20=40hours

 

Shortcut Tricks to Solve Boats and Streams Questions

 

INTRODUCTION:

Downstream: If the boat is moving in the direction of the stream.
Upstream: If the boat is moving in the direction opposite to the direction of the stream.

Assume the speed of the boat in still water as: ‘b’ kilometres per hour (kmph).

Take the speed of the stream as:  ‘s’ kmph.

Hence Aggregate Downstream Speed = b + s kmph. (Boat is moving with the steam of water).

Upstream Net Speed = b – s km/hr. (Boat is moving against the direction of the stream).

Speed of Boat in Still Water:   ½ (Downward Speed + Upward Speed) 

Proof of Basic Formula                 

½ (Downstream Speed + Upstream Speed) = ½ [b + s + (b-s)] = ½ (2b) = b

(Proved as per the assumption)

Speed of Stream:  ½ (Downward Speed – Upward Speed)

Proof of Basic Formula 

½ (Downward Speed – Upward Speed) = ½ [b + s – (b-s)] = ½ [b + s – b + s] = ½ (2 s} = s

(Proved as per the assumption).

 ALWAYS REMEMBER: 

  • Speed of boat is always greater than the speed of the stream.
  • Downstream speed is always greater than the upward speed.

EXAMPLES:

Example 1. 

A man can row a boat @ 9 kmph 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.

Solution:

ATQ (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 kmph Answer.

OR 
Simply
→b + s = 2(b –s)
→i.e. b + s = 2b – 2s
→i.e. s + 2s = 2b –b
Or 
→b = 3s or 9 = 3s (b = 9 is given) = 3 kmph Answer

Example 2.

A boat runs at 20 kmph along the stream and 10 kmph against the stream. Find the ratio of speed of the boat in still water to that of the speed of the stream. 

Solution:

→ ATQ (According to Question) and formula given above:
→ Speed of Boat = ½ (20 + 10) = 15 kmph.
→ Speed of Stream = ½ (20 – 10) = 5 kmph.
→ Ratio: 15:5 = 3:1 Answer. 

Example 3.

Find the time taken by the boatman to row 4 kilometres downstream and return to his starting point, if the speed or rate of stream is 2 kilometres per hour and the speed of the boat is 6 kilometres per hour. 

Solution:

ATQ (According to Question) and formula given above: 
→ Time = Distance/Speed
→ Time taken = 4/6+2 + 4/6-2 = 4/8 + 4/4 = 0.5 + 1 = 1.5 Hour.

Example 4.

If the speed of the stream is 2 km per hour, and the speed of the boat in still waters is 10 km per hour then find the time taken to cover 60 kms downstream.

Solution:

→ ATQ (According to Question) and formula given above:
→ 60/10+2 = 60/12 = 5 hours Answer. 

Example 5.

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. 

Solution:

ATQ (According to Question) and formula given above: 
→ Speed b + s = 60/5 = 12 kmph
→ Speed b = 10 kmph
→ So, speed s = 12-10 = 2 kmph Answer. 

Example 6.

A boat covers a certain distance in one hour downstream with the speed of 10 kmph in still water and the speed of current is 4 kmph. Then find out the distance travelled. 

Solution:

ATQ (According to Question) and formula given above:
→ Distance = Speed x Time = 1 x (10+4) = 14 kms. Answer

Example 7.
A boat takes 6 hours to cover 36 km downstream and 8 hours to cover 32 km upstream. Then the speed of the boat in still water is? 

Solution:

ATQ (According to Question) and formula given above: 
→ Speed of Boat = ½ (36/6 + 32/8) = ½ (6+4) = ½(10) = 5 kmph Answer. 

Example 8.

A boat takes 6 hours to cover 36 km downstream and 8 hours to cover 32 km upstream. Then the speed of the stream is? 

Solution:

ATQ (According to Question) and formula given above:
 Speed of Stream ½ (36/6 – 32/8) = ½ (6-4) = ½ (2) = 1 kmph Answer.

Example 9.

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?

Solution:

ATQ (According to Question) and formula given above: 
→ Speed of Boat in still waters = ½ (6/3 + 2/2) = ½ (2 + 1) = 1.5 kmph
→ Time taken for 9 kms = 9/1.5 = 6 hours Answer

 

1) A man can row 18km/hr in still water. speed of the man in downstream is thrice the speed in upstream. Find the rate of stream.

Solution:

Let, Speed of man in upstream a = a

Speed of man in downstream b = 3a

Speed of man in still water u = ½(a + b)

Speed of man in still water = ½(3a + a) = 2a

We know speed of man in still water = 18

So, a = 9

Rate of stream = ½(27 – 9) =9 km/hr

 

2) A boat can cover certain distance in downstream in 1hr. and it takes 1½hr to cover same distance in upstream. If speed of the stream is 3kmph, then what will be the speed of boat?

Solution:

let speed of boat in still water be x

speed in downstream = x + 3

speed in upstream = x – 3

Since boat covered same distance in upstream and downstream,

(x + 3)*1 = (x – 3)*(3/2)

speed in downstream x= 15 kmph

 

3) A man can row three quarter of a km against the stream in 11¼ min and down the stream in 7½min. what is the speed of man in still water.

Solution:

Speed of man in Upstream = ((¾)/(45/4)) *60

= 4 kmph

Speed of man in Downstream = ((¾)/(15/4))* 60

= 12 kmph

Speed of man in still water u = ½(a + b)

Speed of man in still water = (12 + 4)*½ = 8 kmph

 

4) A streamer takes 3hr to cover a distance of 24km upstream, if the rate of stream is 3 kmph. Then find the speed of streamer in still water.

Solution:

Upstream speed = 24/3 =8kmph

Rate of stream = 3kmph

Speed of streamer – rate of stream = upstream

Speed of streamer = 11kmph

 

5) The distance between two points is 36km. A boat rows in still water at 6kmph, it takes 8hr less to cover dist in downstream in comparison to that in upstream. Find the rate of stream.

Solution:

Time = distance * speed

Difference between time taken to cover upstream and downstream is 8hr

(36/(6-x)) – (36/(6+x)) = 8

36(6+x) – 36(6-x) = 8(36-x2)

9x = 36- x2

x2+9x-36 = 0 (to find value of x use quadratic equation technique)

(x+12)(x-3)=0

Speed cannot be negative so x = 3kmph

Rate of stream = 3kmph

 

Types of Questions asked in Previous Exam

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)

Example:  

A man can row 9km/h in still water. It takes him twice as long as to row up as to row down. Find the rate of the stream of the river.

Solution:

Time taken in upstream : Time taken in Downstream = 2 : 1

Downstream speed : Upstream speed = 2 : 1

Let the speed of man = B, & speed of stream = S

B + S : B – S = 2/1

By using Componendo & Dividendo

B/R = 3/1, R = B/3

R = 9/3 = 3km/h
Type 2: A boat cover certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of stream is y km/h, then the speed of the boat in still water is:

Short Trick:

Speed of Boat = y [(t2 + t1) / (t2 – t1)]

Example

A man can row certain distance downstream in 2 hours and returns the same distance upstream in 6 hours. If the speed of stream is 1.5 km/h, then the speed of man in still water is

Solution:

By using above formulae

= 1.5 [(6+2) / (6-2)] = 1.5 * (8/4) = 1.5 * 2 = 3km/h

 

Type 3: A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it takes it t hours to row to a place and come back, then the distance between two places is

Short Trick:   Distance = [t*(x2 – y2)]/2x

Example

A motor boat can move with the speed 7 km/h. If the river is flowing at 3 km/h, it takes him 14 hours for a round trip. Find the distance between two places?

Solution: By using above formulae

                = [14 * (72 – 32)]/2* 7 = [14 * (49-9)]/2*7

= 14*40/2*7 = 40km

 

Type 4:  A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance is

Short Trick: Distance = [t*(x2 – y2)]/2y

Example

A professional swimmer challenged himself to cross a small river and back. His speed in swimming pool is 3km/h. He calculated the speed of the river that day was 1km/h. If it took him 15 mins more to cover the distance upstream than downstream, then find the width of the river?

Solution: By using the above formulae

Distance = [t*(x2 – y2)]/2y

= [(15/60) (32 – 12)]/2*1

= [(1/4) * 8] / 2

= 2/2 = 1 km.

 

Type 5: A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it cover the same distance up and down the stream, then its average speed is

Short Trick: Average speed = upstream * downstream / man’s speed in still water

Note: The average speed is independent of the distance between the places.

Example

Find the average speed of a boat in a round trip between two places 18 km apart. If the speed of the boat in still water is 9km/h and the speed of the river is 3km/h?

Solution: Average speed = upstream * downstream / man’s speed in still water

Average speed = 6 * 12 / 9 = 8km/h

 

Problem Set For Boat & Stream



 

  • A boat takes 28 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 6km/hr and the speed of the boat in still water is 9 km/hr, what is the distance between A and B?
    A.115 km
    B.120 km
    C.140 km
    D.165 km
    E.150 km

    Answer & Explanation
    Answer – B.120 km
    Explanation :
    Downstream speed = 9+6 = 15
    Upstream speed = 9-6 = 3
    Now total time is 28 hours
    If distance between A and B is d, then distance BC = d/2
    Now distance/speed = time, so
    d/15 + (d/2)/3= 28
    Solve, d = 120 km
  • Speed of a man in still water is 5 km/hr and the river is running at 3km/hr. The total time taken to go to a place and come back is 10 hours. What is the distance travelled?
    A.10 km
    B.16 km
    C.24 km
    D.32 km
    E.36 km

    Answer & Explanation
    Answer – D.32 km
    Explanation :
    Down speed= 5+3= 8
    Up speed= 5-3=2
    Let distance travelled = X
    (X/8)+(X/2)= 10
    X= 16 km
    Total distance is 16+16=32
  • A boat running upstream takes 9 hours 48 minutes to cover a certain distance, while it takes 7 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
    A.5:2
    B.7:4
    C.6:1
    D.8:3
    E.2:5

    Answer & Explanation
    Answer – C.6:1
    Explanation :
    Distance covered upstream in 9hrs 48 min = Distance covered downstream in 7hrs
    (X-Y) 49/5=(X+Y)7
    X/y=1/6
  • A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?
    A.20 min
    B.22 min
    C.25 min
    D.30 min
    E.35 min

    Answer & Explanation
    Answer – D.30 min
    Explanation :
    Down speed =20/24*60=50km/hr
    4:1 =4x:x
    Downstream speed = 4x+x=5x
    Upstream speed = 4x-x=3x
    5x= 50; x=10
    so up speed 3*10=30
    Time = 15/30*60= 30min.
  • A boat whose speed in 20 km/hr in still water goes 40 km downstream and comes back in a total of 5 hours. The approx. speed of the stream (in km/hr) is:
    A.6 km/hr
    B.9 km/hr
    C.12 km/hr
    D.16 km/hr
    E.18 km/hr

    Answer & Explanation
    Answer – B.9 km/hr
    Explanation :
    Let the speed of the stream be x km/hr. Then,
    Speed downstream = (20 + x) km/hr,
    Speed upstream = (20 – x) km/hr.
    40/20+x + 40/20-x = 5
    X = 9 approx
  • A boat covers a certain distance downstream in 2 hour, while it comes back in 2 1/2 hours. If the speed of the stream be 5 kmph, what is the speed of the boat in still water?
    A.40 kmph
    B.30 kmph
    C.35 kmph
    D.45 kmph
    E.None of these

    Answer & Explanation
    Answer – D.45 kmph
    Explanation :
    Let the speed of the boat in still water be x kmph. Then,
    Speed downstream = (x + 5) kmph,
    Speed upstream = (x – 5) kmph.
    (x + 5)*2 = (x – 5)*5/2
    X = 45 kmph
  • A boat running downstream covers a distance of 40 km in 5 hrs and for covering the same distance upstream it takes 10 hrs. What is the speed of the stream? 
    A.5 km/hr
    B.2 km/hr
    C.6 km/hr
    D.4 km/hr
    E.3 km/hr

    Answer & Explanation
    Answer – B.2 km/hr
    Explanation :
    Downstream speed = 40/5 = 8 km/hr
    Upstream speed = 40/10 = 4 km/hr
    So speed of stream = 1/2*(8-4)
  • A boat goes 4 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 15 km in stationary water?
    A.2 hour 15 min
    B.2 hour
    C.3hr
    D.3hr 30 min
    E.None of these

    Answer & Explanation
    Answer – C.3hr
    Explanation :
    Rate downstream = 1/10 * 60 = 6kmph
    Rate upstream = 4 km/hr.
    Speed in still water = ½ * 10 = 5 kmph
    Required time = 15/5 = 3 hr
  • A man rows to a place 40 km distant and come back in 9 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. The rate of the stream is:
    A.1 km/hr
    B.1.5 km/hr
    C.2 km/hr
    D.2.5 km/hr
    E.None of these

    Answer & Explanation
    Answer – A.1 km/hr
    Explanation :
    Speed downstream = 5/x
    Speed upstream = 4/x
    40/(5/x) + 40/(4/x) = 9
    X = ½
    So, Speed downstream = 10 km/hr, Speed upstream = 8 km/hr.
    Rate of the stream = 1/2 * 2 = 1 kmph
  • A man can row 8 km/hr in still water. When the river is running at 4 km/hr, it takes him 2 1/3hr to row to a place and come back. How far is the place?
    A.4 km
    B.5 km
    C.7 km
    D.10 km
    E.None of these

    Answer & Explanation
    Answer – C.7 km
    Explanation :
    Downstream speed = 8+4= 12 => a
    Upstream speed = 8-4= 4 => b
    Distance = a*b/(a+b) * total time (t)
    = 12*4/16 * 7/3
    = 7kms

 

  • If Nishu can swim downstream at 6kmph and upstream at 2kmph.What is his
    speed in still water ?
    A.5 km/hr
    B.4 km/hr
    C.8km/hr
    D.7km/hr

    Answer
    Answer- B
    Basic Formula:

    If the speed downloadstream is a km/ hr and the speed upstream is b km/ hr
    then Speed in still water is = ½ (a+b) km / hr [memory tool last 2 L cross and make +]            
    Explanation:
    Given : speed downstream a = 6 km ph
    Speed upstream b = 2kmph
    Speed in still water = ½ (a+b) kmph
    = ½ (6+2)
    = 8/2 = 4kmph
    speed in still water = 4kmph
  • Ashok can row upstream at 8kmph and downstream at 12kmph.What is the
    speed of the stream ?
    A.6km/hr
    B.3km/h
    C.2 km/hr
    D.4km/hr

    Answer
    Answer -C 
    Basic Formula:
    If the speed downstream is a kmph and the speed upstream is b kmph
    then
    Speed of the stream = ½ (a-b) kmph
    Explanation:
    Speed downstream a = 12kmph
    Speed upstream b = 8 kmph
    Speed of the stream = ½ (a-b) = ½ (12-8)
    = 4/2 = 2 kmph
    speed of the stream = 2kmph
  • A man rows 750m in 775 seconds against the stream and returns in 7
    1/2 minutes. What is rowing speed in still water ?
    A.4.7km/hr
    B. 4km/hr
    C.3.5km/hr
    D.6km/hr

    Answer
    Answer-A 
    Basic Formula:
    i) Speed in still water = ½ (a+b) kmph where ‘a’ is speed
    downstream and ‘b’ is speed upstream
    ii) a km / hr = a x 5/18 m /s
    iii) a m/sec = a x 18/5 km/hr
    Explanation:
    Speed upstream ‘b’ = 750m / 775 sec = 30/31 m/sec
    Speed downstream ‘a’ = 750 m/ (15/2)minutes [ 1min=60 sec] a = 750m/450 sec =5/3 m/sec
    speed in still water = ½ (a+b)
    = ½ (750/450 + 750/675 ) m /sec
    = ½ (750/450 + 750/675 ) x 18/5 km/hr
    = ½ (5/3 + 30/31) x 18/5 km/hr
    = 4.7 km/hr
  • A man can row 9 (1/3) kmph in still water and finds that it takes him
    thrice as much time to row up than as to row down the same distance in the
    river. What is speed of the current ?
    A. 5km/hr
    B.3(1/2) km/hr
    C.4 (2/3) km/hr
    D.8 (3/2)km/hr

    Answer
    Answer- C
    Basic Formula:
    Speed of current = ½ (a-b) km/hr
    Explanation:
    Let man’s rate upstream be x km/hr. Then his rate downstream is 3 x km/hr
    Given:
    Speed in still water = 9 (1/3) = 28/3 km/hr
    i.e, ½ (a+b) = 28/3 km/hr
    ½ (x+3x) = 28/3
    2x = 28/3    x = 28/ 2 x 3 = 14/3 km/hr
    rate upstream b = 14/3 km/hr and
    rate downstream a = 14/3 x 3 = 14 km/hr
    speed of the current = ½ (a-b) = ½ (14 – 14/3)
    = ½ (42-14/3) = 28/6 = 4 (2/3) km/hr
  • Sham can row a boat at 10kmph in still water. IF the speed of the
    stream is 6kmph, the time taken to row a distance of 80km down the stream
    is
    A.4 hours
    B.5hours
    C.3 hours
    D.2 hours

    Answer
    Answer- B
    Basic Formula:
    Speed of stream = ½ (a-b) km/hr
    Speed in still water = ½ (a+b) km/hr
    Explanation:
    Given:
    Speed in still water, ½ (a+b) = 10 km/hr
    a+b = 20 km/hr…………….(1)
    speed of the stream, ½ (a-b) = 6km/hr
    a-b = 12 km/hr …………….(2)
    (1)+(2 ) we get 2a = 32
    a = 16 km/hr
    speed downstream =distance traveled / time taken
    time taken = 80/16 = 5 hours
  • A boat takes 4hours for traveling downstream from point P to point
    Q and coming back to point P upstream. If the velocity of the stream is 2km
    ph and the speed of the boat in still water is 4kmph, what is the distance
    between P and Q?
    A.9 km
    B.7 km
    C.5 km
    D.6km

    Answer
    Answer- D
    Basic Formula:
    Speed of stream = ½ (a-b) km/hr
    Speed of still water = ½ (a+b) km/hr
    Explanation:
    Time taken by boat to travel upstream and downstream = 4 hours
    Velocity of the stream, ½ (a-b) = 2km/hr
    a-b = 4km/hr ……………….( 1)
    velocity of the boat in still water = ½ (a+b) = 4km/hr
    a+b = 8 km/hr ………………(2)
    1 +2 we get a = 6 km/hr ,b = 2km/hr
    let the distance between A and B be x km
    x / 2 + x / 6 = 4
    3x + x / 6 = 4  4x = 24 so,x = 6
    distance between P and Q = 6km
  • Speed of a boat in standing water is 9kmph and the speed of the
    stream is 1.5kmph. A man rows to a place at a distance of 10.5 km and
    comes back to the starting point. Find the total time taken by him.
    A.24 hours
    B.16 hours
    C.20 hours
    D.15 hours

    Answer
    Answer- A
    Basic Formula:
    i. speed = distance traveled / time taken
    ii. speed of the stream = ½ (a-b) km/hr
    iii. speed in still water = ½ (a+b) km/hr
    Explanation:
    Speed in still water= ½ (a+b) = 9km ph
    = a+b = 18 …………….1
    speed of the stream = ½ (a-b) = 1.5 kmph
    = a-b = 3 kmph…………2
    solving 1 and 2 gives a = 10.5km/hr ; b=7.5 kmphr
    Total time taken by him = 105/10.5 + 105/7.5 = 24 hours
  • A man rows to a place 48km distant and back in 14 hours. He finds
    that he can row 4km with the stream in the same time as 3km against the
    stream. Find the rate of the stream.
    A.2 km/hr
    B.1 km/hr
    C.3 km/hr
    D.3.5km/hr

    Answer
    Answer- B
    Basic Formula:
    Speed of the stream = ½ (a-b) km / hr
    Speed = distance traveled / time taken
    Explanation:
    Suppose he moves 4km downstream in x hours
    Then, downstream a= 4 / x km/hr
    Speed upstream b = 3/ x km/hr
    48 / (4 /x) + 48 / (3/x) = 14
    12x + 16x = 14
    x = 1/2
    a=8 km/hr ,b = 6 km/hr
    rate of stream = ½ (8 – 6 )
    =  1 km/hr
  • There is road besides a river. Two friends started from a place P, moved to a shopping mall
    situated at another place Q and then returned to P again. One of them moves on a cycle at
    a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river
    flows at the speed of 4 km/hr, which of the two friends will return to place P?
    A. Both
    B. Boater
    C. Cyclist
    D. None of these

    Answer
    Answer-C
    Explanation:
    The cyclist moves both ways at a speed of 12khr so average speed fo the
    cyclist – 12 km/hr
    boat sailor moves downstream at 10+4 = 14km/hr and upstream 10-
    4 = 6km/hr
    Average speed of the boat sailor = 2 x 14 x 6 / 14 +6 = 42/ 5 = 8.4km/hr
    The average speed of cyclist is greater .so,cyclist comes first and return to
    place P.
  • A this usual rowing rate, Mohit can travel 12 miles downstream in a certain river in 6
    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.2.5m/hr
    B.4 m/hr
    C.8/3 m/hr
    D. 5/3m/hr

    Answer
    Answer-C
    Basic Formula:
    Speed of the stream = ½ (a-b) km/hr
    Explanation:
    Let the speed in still water be x m/hr
    Speed of stream be y m/hr
    Then, speed upstream = x-y m/hr and
    Speed downstream = x+y m/hr
    12/x-y – 12 / x+y = 6 so,6 (x^2 – y^2) = 24 y
    x^2 – y^2 = 4y
    x^2 = y^2 + 4y…………..1
    also
    12/ 2x-y – 12/2x +y = 1 4x^2 – y^2 = 24y
    x^2 = [24y + y^2] / 4 ……………….2
    16y + 4y^2 = 24y + y2 [put X^2 value from 1] 3y^2 = 8 y so, y = 8/3
    speed of the current = 8/3 m/hr = 2 (2/3) m/hr

 

  • A boat can travel 15 km downstream in 18 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 10 km upstream?
    A) 22 min
    B) 25 min
    C) 20 min
    D) 33 min
    E) 30 min

    Answer & Explanation
    C) 20 min
    Explanation: 

    Use:
    B = [tu + td] / [tu – td] * R
    15 km downstream in 18 min so 10 km in (18/15)*10 = 12 min
    B= 4x, R = x
    Now
    4x = [tu + 12] / [tu – 12] * x
    Solve, tu = 20 min
  • Speed of a man in still water is 4 km/hr and the river is running at 2 km/hr. The total time taken to go to a place and come back is 4 hours. What is the distance travelled? 
    A) 16 km
    B) 13 km
    C) 10 km
    D) 6 km
    E) 8 km

    Answer & Explanation
    D) 6 km
    Explanation: 

    Use
    Distance = time * [B^2 – R^2] / 2*B
    Distance = 4* [4^2 –2^2] / 2*4
  • A boat takes 25 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 5 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B? 
    A) 100 km
    B) 122 km
    C) 146 km
    D) 178 km
    E) 150 km

    Answer & Explanation
    E) 150 km
    Explanation: 

    Downstream speed = 10+5 = 15
    Upstream speed = 10-5 = 5
    Now total time is 25 hours
    If distance between A and B is d, then distance BC = d/2
    Now distance/speed = time, so
    d/15 + (d/2)/5= 25
    Solve, d = 150 km
  • A boat goes 6 km against the current of the stream in 2 hours and goes 8 km along the current in half hour. How long will it take to go 28.5 km in stationary water? 
    A) 4 1/2 hours
    B) 3 hours
    C) 3 1/2 hours
    D) 4 hours
    E) None of these

    Answer & Explanation
    B) 3 hours
    Explanation: 

    Speed upstream = 6/2 = 3, speed downstream = 8/(1/2) = 16
    Speed of boat = 1/2(3+16) = 9.5 km/hr
    So time in still water = 28.5/9.5
  • A man can row 48 km upstream and 56 km downstream in 12 hrs. Also, he can row 54 km upstream and 70 km downstream in 14 hrs. What is the speed of man in still water? 
    A) 4 km/hr
    B) 10 km/hr
    C) 12 km/hr
    D) 15 km/hr
    E) 18 km/hr

    Answer & Explanation
    B) 10 km/hr
    Explanation: 

    Let upstream speed = x km/hr, downstream speed = y km/hr
    So 48/x + 56/y = 12
    And 54/x + 70/y = 14
    Put 1/x = u, 1/y = v
    So equations are 48u + 56v = 12 and 54u + 70v = 14
    Solve the equations, u = 1/6, v = 1/14
    So upstream speed = 6 km/hr, downstream speed = 14 km/hr
    Speed of boat in still water = 1/2*(6+14)
  • A boat takes 150 min less to travel 40 km downstream than to travel the same distance upstream. The speed of the stream is 4 km/hr. What is the downstream speed? 
    A) 16 km/hr
    B) 12 km/hr
    C) 10 km/hr
    D) 8 km/hr
    E) None of these

    Answer & Explanation
    A) 16 km/hr
    Explanation: 

    Let speed of boat in still water = x km/hr
    So speed upstream = x-4, and speed downstream = x+4
    Now given:
    Time to travel 40 km downstream = time to travel 40 km upstream – 150/60
    So 40/(x+4) = 40/(x-4) – 5/2
    8/(x-4) – 8/(x+4) = 1/2
    x+4 – (x-4)/(x2 – 16) = 1/16
    solve, x = 12
    so downstream speed = 12+4
  • A man rows to a place 40 km distant and back in a total of 18 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. What is the speed of boat in still water? 
    A) 4.5 km/hr
    B) 8 km/hr
    C) 5.5 km/hr
    D) 2 km/hr
    E) None of these

    Answer & Explanation
    A) 4.5 km/hr
    Explanation: 

    Suppose he moves 5km downstream in x hours
    Then, downstream speed a= 5/x km/hr
    Speed upstream speed b = 4/x km/hr
    40 / (5 /x) + 40 / (4/x) = 18
    8x + 10x = 18
    x = 1
    a = 5 km/hr, b = 4 km/hr
    speed of boat = ½ (5 + 4 ) = 9/2 km/hr
  • In a stream running at 2 km/hr, a motorboat goes 6 km upstream and back again to the starting point in 2 hours. Find the speed of boat in still water. 
    A) 9 km/hr
    B) 12 km/hr
    C) 8 km/hr
    D) 10 km/hr
    E) None of these

    Answer & Explanation
    C) 8 km/hr
    Explanation: 

    Distance = time * [B^2 – R^2] / 2*B
    6 = 2 * [B^2 – 4^2] / 2*B
    B^2 – 6B – 16 = 0
    (B-8)(B+2) = 0
    So B = 8
  • It takes five times as long to row a distance against the stream as to row the same distance in favor of the stream. What is the ratio of the speed of the boat in still water to that of stream? 
    A) 7 : 4
    B) 2 : 3
    C) 9 : 5
    D) 3 : 2
    E) 5 : 2

    Answer & Explanation
    D) 3 : 2
    Explanation: 

    Use:
    B = [tu + td] / [tu – td] * R
    So
    B =[5x + x] / [5x- x] * R
    So B/R = 6/4 = 3/2
  • A boat running downstream covers a distance of 32 km in 4 hrs and for covering the same distance upstream it takes 8 hrs. What is the speed of the stream? 
    A) 5 km/hr
    B) 2 km/hr
    C) 6 km/hr
    D 4 km/hr
    E) 3 km/hr

    Answer & Explanation
    B) 2 km/hr
    Explanation: 

    Downstream speed = 32/4 = 8 km/hr
    Upstream speed = 32/8 = 4 km/hr
    So speed of stream = 1/2*(8-4)

 

  • A boat can travel 4.2km upstream in 14min. If the ratio of the speed of the boat in still water to the speed of the stream is 7:1. How much time will the boat take to cover 17.6km downstream ?
    A)56min
    B)44min
    C)32min
    D)48min
    E)None of these

    Answer
    B)44min
    Explanation :
    Speed = 7x:x
    Downstream = 8x; upstream = 6x
    Upstream speed = 4.2*60/14 = 18kmph
    6x = 18
    X = 3
    Downstream = 8*3 = 24
    Time taken for 17.6km = 17.6*60/24 = 44min
  •  A man can row at 4 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.
    A)1.8km
    B)2.6km
    C)1.5km
    D)3.2km
    E)None of these

    Answer
    A)1.8km
    Explanation :
    Let the distance is x km
    Rate downstream = 4 + 1 = 5 kmph
    Rate upstream = 4 – 1 = 3 kmph
    then
    x/5 + x/3 = 1
    3x + 5x = 15
    x = 15/8 = 1.8 km
  • Arun  takes thrice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and stream is
    A)3:1
    B)1:2
    C)2:1
    D)2:3
    E)None of these

    Answer
    C)2:1
    Explanation :
    speed downstream = x kmph
    Speed upstream = 3x kmph
    (3x+x)/2 : (3x-x)/2
    4x/2 : 2x/2 = 2:1
  • A boat takes 30 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 2 kmph and the speed of the boat in still water is 15 kmph, what is the distance between A and B?
    A)342km
    B)356km
    C)316km
    D)308km
    E)None of these

    Answer
    D)308km
    Explanation :
    velocity of the stream = 2 kmph
    Speed of the boat in still water is 15 kmph
    Speed downstream = (15+2) = 17 kmph
    Speed upstream = (15-2) = 13 kmph
    Let the distance between A and B be x km
    x/17+(x/2)/13=30
    x/17+x/26=30
    43x/442=30
    x=30*442/43 = 308.37 = 308km
    distance between A and B = 308 km
  • A boat takes 120min less to travel 30km downstream than to travel the same distance upstream.If the speed of the boat in still water is 8kmph then the speed of the stream is
    A)2kmph
    B)8kmph
    C)3kmph
    D)4kmph
    E)None of these

    Answer
    A)2kmph
    Explanation :
    Speed of the stream = x
    (30/8-x) – (30/8+x)= 120/60 = 2/1
    30(8+x) – 30(8-x) = 2[64 – x2] 240+30x-240x+30x = 2[64 – x2] 60x = 128- 2x2
    2x2+60x-128 = 0
    x2+30x-64 = 0
    (x+32)(x-2) = 0
    X=2kmph
  • A boat running downstream covers a distance of 24km in 4hrs, while for covering
    the same distance upstream it takes 6hrs, what is the speed of the boat in still water ?
    A)12kmph
    B)10kmph
    C)5kmph
    D)7kmph
    E)None of these

    Answer
    C)5kmph
    Explanation :
    24/x-y = 6
    6x – 6y = 24………….(1)
    24/x+y = 4
    4x+4y = 24………….(2)
    24x – 24y = 96
    24x+24y = 144
    Solve abv 2 equ
    48x = 240
    X = 240/48 = 5
  • A man swims downstream 40 km in 5 hours and upstream 24 km in 2 hours. Find his speed in still water ?
    A)10kmph
    B)15kmph
    C)8kmph
    D)12kmph
    E)None of these

    Answer
    A)10kmph
    Explanation :
    Downstream  = 40/5= 8 kmph
    Upstream = 24/2== 12 kmph
    Speed in still water = 1/2 ( 8+12) = 10 kmph
  • The speed of a boat in still water in 12 km/hr and the rate of current is 4 km/hr. The
    distance travelled downstream in 12 minutes is
    A)3.2km
    B)4.7km
    C)5.1km
    D)2.7km
    E)None of these

    Answer
    A)3.2km
    Explanation :
    Speed downstream = (12 + 4) kmph = 16 kmph.
    Distance travelled = 16 x12/60 km = 3.2 km
  • A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
    A)1.30hrs
    B)3.209hrs
    C)2.15hrs
    D)1.25hrs
    E)None of these

    Answer
    D)1.25hrs
    Explanation :
    downstream =(1x 60)/10  = 6 kmph
    Rate upstream = 2 km/hr.
    Speed in still water =(6 + 2) /2= 4 kmph
    time = 5/4 =  1.25hrs
  • A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is 
    A)10kmph
    B)4kmph
    C)6kmph
    D)8kmph
    E)None of these

    Answer
    A)10kmph
    Explanation :
    speed of the boat in still water = x kmph
    speed of the current = y kmph
    upstream speed = (x – y) kmph
    downstream speed = (x + y)kmph
    24/(x-y) + 28/(x+y) = 6
    30/(x-y) + 21(x+y) = 13/2
    X = 10kmph

 

  • A man can row upstream at 10 km/hr and downstream at 16 km/hr. Find the man’s rate in still water and the rate of current. 
    A. 13 km/hr, 3 km/hr
    B. 10 km/hr, 2 km/hr
    C. 3 km/hr, 13 km/hr
    D. 15 km/hr, 5 km/hr

    Answer
    A. 13 km/hr, 3 km/hr
    Explanation:
    man’s rate in still water = 1/2 (16+10)
    man’s rate in still water = 1/2 (16+10)
  • A boat can row at 16 km/hr in still water and the speed of river is 10 km/hr. Find the speed of boat with the river and speed of boat against the river. 
    A. 13 km/hr, 3 km/hr
    B. 15 km/hr, 5 km/hr
    C. 26 km/hr, 6 km/hr
    D. 6 km/hr, 26 km/hr

    Answer
    C. 26 km/hr, 6 km/hr
    Explanation:
    Speed with the river (downstream) = 16+10
    Speed against the river (upstream) = 16-10
  • A man goes downstream 60 km and upstream 20 km, taking 4 hrs each. What is the velocity of current?
    A. 4 km/hr
    B. 8 km/hr
    C. 6 km/hr
    D. 5 km/hr

    Answer
    D. 5 km/hr
    Explanation:
    Downstream speed = 60/4 = 15 km/hr
    Upstream speed = 20/4 = 5 km/hr
    Velocity of stream = (15-5)/2 = 5 km/hr
  • A man rows downstream 28 km and upstream 16 km, taking 5 hrs each time. What is the velocity of current?
    A. 4 km/hr
    B. 2.4 km/hr
    C. 1.2 km/hr
    D. 3 km/hr

    Answer
    C. 1.2 km/hr
  • A man can row 30 km upstream and 44 km downstream in 10 hrs. Also, he can row 40 km upstream and 55 km downstream in 13 hrs. Find the speed of the man in still water.
    A. 5 km/hr
    B. 8 km/hr
    C. 10 km/hr
    D. 12 km/hr

    Answer
    B. 8 km/hr
    Explanation:
    Let upstream speed = x, downstream speed = y km/hr
    Then, 30/x + 44/y = 10 and 40/x + 55/y = 13
    Put 1/x = a, 1/y = b
    Solve the equations.
    A = 1/5, b = 1/11
    So, x = 5, y = 11
    Speed in still water = (5+11)/2 = 8
  • A man can row 24 km upstream and 36 km downstream in 6 hrs. Also, he can row 36 km upstream and 24 km downstream in 6.5 hrs. Find the speed of the current.
    A. 2 km/hr
    B. 8 km/hr
    C. 10 km/hr
    D. 12 km/hr

    Answer
    A. 2 km/hr
  • A man can row 6 km/hr in still water. When the river is running at 2 km/hr, it takes him 1 ½ hr to row to a place and come back. How far is the place?
    A. 2.5 km
    B. 4 km
    C. 5 km
    D. 10 km

    Answer
    B. 4 km
    Explanation:
    B is speed of boat in still water, R is speed of stream
    Time is total time taken for upstream and downstream
    Distance = time * [B^2 – R^2] / 2*B
    =3/2 * [6^2 – 2^2] / 2*6
  • In a stream running at 2 km/hr, a motorboat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed (km/hr) of the motorboat in still water.
    A. 17
    B. 20
    C. 22
    D. 25

    Answer
    C. 22
    Explanation:
    Distance = time * [B^2 – R^2] / 2*B
    10 =55/60 * [B^2 – 2^2] / 2*B
  • A man can row a certain distance downstream in 2 hours and return the same distance in 6 hours. If the speed of current is 22 km/hr, find the speed of man in still water.
    A. 44km/hr
    B. 48 km/hr
    C. 50 km/hr
    D. 55 km/hr

    Answer
    A. 44km/hr
    Explanation:
    Use:
    B = [tu + td] / [tu – td] * R
    B = [6+2] / [6-2] * 22
    B = 44
  • A man can row 9 3/5 km/hr in still water and he finds that it takes him twice as much time to row up than as to row down the same distance in river. The speed (km/hr) of the current is 
    A. 2
    B. 2 1/2
    C. 3 1/5
    D. 5

    Answer
    C. 3 1/5
    Explanation:
    Let downstream time = t, then upstream time = 2t
    B = [tu + td] / [tu – td] * R
    48/5 = [2t+t] / [2t-t] * R

 

 

 

 

 

 

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