padhlebeta.net aptitude boats and streams

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PadhleBeta.net For further information please contact: [email protected] Aptitude - Boats and Streams ------------------------------------- In this section you will find aptitude questions and answers of various difficulty levels on Boats and Streams with explanation for various interview, competitive examination and entrance test in an easy to understand way. You can also checkout Tips and Tricks, Videos related to the topic.Use Green Board or space provided for Rough work whenever you need. Formulae : Boats and Streams: A Boat is said to be moving downstream when it is going with the stream and it is said to be going upstream if it is going against the stream. If the speed of Boat in still water is x km/h and speed of stream is y km/h Then speed of Boat downstream is = (x y) km/h And , Speed of Boat upstream is = (x-y) km/h. If we are provided with the speed of boat downstream and upstream , then to find the speed of boat in still water we use Speed of boat in still water = 1/2( downstream upstream) And to find speed of stream we use

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Page 1: PadhleBeta.net Aptitude Boats and Streams

PadhleBeta.netFor further information please contact: [email protected]

Aptitude - Boats and Streams

-------------------------------------In this section you will find aptitude questions and answers of various

difficulty levels on Boats and Streams with explanation for various interview,

competitive examination and entrance test in an easy to understand way. You can

also checkout Tips and Tricks, Videos related to the topic.Use Green Board or

space provided for Rough work whenever you need.

Formulae :Boats and Streams:

A Boat is said to be moving downstream when it is going with the stream

and it is said to be going upstream if it is going against the stream.

If the speed of Boat in still water is x km/h and speed of stream is y km/h

Then speed of Boat downstream is = (x y) km/h

And ,

Speed of Boat upstream is = (x-y) km/h.

If we are provided with the speed of boat downstream and upstream ,

then to find the speed of boat in still water we use

Speed of boat in still water = 1/2( downstream upstream)

And to find speed of stream we use

Page 2: PadhleBeta.net Aptitude Boats and Streams

Speed of stream = 1/2 (downstream - upstream)

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----------------------------------------------------------------------------------

Formulae:

A)A person rows a boat to a certain place and then comes back to the

straight point . If he rows the boat at the speed of ‘x’ km/h in still water

and the rate of the current is ‘y’ km/h , then

a.Average speed during the journey = 2(x y)(x-y) / {(x y) (x-y)} = 2(x2-y2)

/ 2x = (x2-y2) / x | Here x y and x-y are the speeds of boat downstream

and upstream respectively.

b.If the ratio of downstream and upstream speeds of a boat is a:b then

i.Ratio of time taken is = b:a and ,

ii.Speed of stream is = Speed in still water X {(a-b)/(a b)}

iii.Speed in still water is = Speed of stream X {(a b)/(a-b)}

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Proof:

Let speed of boat in still water be = x km/h

And speed of the stream be = y km/h

Speed of boat downstream = (x y) km/h

Speed of boat upstream = (x-y) km/h

(x y) : (x-y) = a:b

Therefore b(x y) = a(x-y) ;

Then y = {(a-b)/(a b)} * x

Where x is Speed of Boat in still water.

Questions and Answers :

Page 3: PadhleBeta.net Aptitude Boats and Streams

PadhleBeta.net - Aptitude - Boats and Streams

1) Rahul rows downstream 32 km and 14 km upstream. If he takes 6

hours to cover each distance, then the velocity (in kmph) of the current

is:

1) 2 kmph 3) 1.5 kmph

2) 1.2 kmph 4) 3 kmph

Solution :

Rate downstream = [32/6] kmph;

Rate upstream = [14/6] kmph.

Velocity of current = 1/2[32/6 - 14/6] kmph

= 3/2 kmph = 1.5 kmph.

PadhleBeta.net - Aptitude - Boats and Streams

2) Arpit can row three-quarters of a kilometer against the stream in 11

1/4 minutes.  speed (in km/hr) of Arpit in still water is:

1) 5 km/hr 3) 46/4 km/hr

2) 51/5 km/hr 4) 8 km/hr

Solution :

Rate upstream = [750 / 675] m/sec = 10/9 m/sec.

Rate downstream = [750 / 450] m/sec = 5/3 m/sec.

Rate in still water = 1/2 [10/9 + 5/3] m/sec

Page 4: PadhleBeta.net Aptitude Boats and Streams

= 25/18 m/sec = [25/18 * 18/5] km/hr

= 5 km/hr

PadhleBeta.net - Aptitude - Boats and Streams

3) A boat running upstream takes 8 hours 48 minutes to cover a certain

distance, while it take 4 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?

1) 8.3 3) 8.8

2) 7 4) 5

Solution :

Let the man rate upstream be x kmph and that downstream be ykmph.

Then,

Distance coverd upstream in 8 hrs 48 min. = Distance coverd

downstream in 4 hrs.

[x 8 4/5] = (y * 4) 44/5 x = 4y  y = 11/5 x.

Required ratio = [y + x / 2] : [6x / 5 * 1/2] : [6x / 5 * 1/2]

= 8/5 : 3/5 = 8:3.

PadhleBeta.net - Aptitude - Boats and Streams

4) Sachin can row 7 1/2 km/hr in still water. If in a river running at 1.5 km

an hour, it takes him 50 minutes to row to a place and back, how far off

is the place?

1) 1 km 3) 4 km

2) 8 km 4) 3 km

Page 5: PadhleBeta.net Aptitude Boats and Streams

Solution :

Speed downstream = (7.5 + 1.5) kmph = 9 kmph;

Speed upstream = (7.5 - 1.5) kmph = 6 kmph.

Let the required distance be x km. Then,

x/9 + x/6 = 50/60 2x + 3x = [5/6 * 18] 5x = 15  x =3. 

Hence, the required distance is 3 km.

PadhleBeta.net - Aptitude - Boats and Streams

5) Find the speed of the boat in still water (in km/hr), If in one hour, a

boat goes 11 km along the stream and 5 km against the stream. 

1) 8 kmph 3) 11 kmph

2) 21 kmph 4) 5 kmph

Solution :

Speed in still water = 1/2 (11+5) kmph

 = 8 kmph.

PadhleBeta.net - Aptitude - Boats and Streams

6) Find the speed of the stream , If the speed of a boat in still water is 10

km/hr. and it can travel 26 km downstream and 14 km upstream in the

same time.

1) 2.4 3) 1.5

2) 3 4) 2

Page 6: PadhleBeta.net Aptitude Boats and Streams

Solution :

Let the speed of the stream be x km/hr. Then, 

Speed downstream = (10+x) km/hr, Speed upstream = (10 - x) km/hr.

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

 x = 3 km/hr.

PadhleBeta.net - Aptitude - Boats and Streams

7) 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?

1) 1 hour 25 min 3) 1 hour

2) 45 minutes 4) 1 hour 15 min

Solution :

Rate downstream = [16/2] kmph = 8 kmph;

Rate upstream = [16/4] kmph = 4 kmph.

Speed in still water = 1/2(8+4) kmph

= 6 kmph.

PadhleBeta.net - Aptitude - Boats and Streams

8) Find the speed of the boat in still water, If a boat covers a certain

distance downstream in 1 hour, while it comes back in 11/2   hours. If the

speed of the stream be 3 kmph. 

1) 12 kmph 3) 18 kmph

2) 15 kmph 4) 22 kmph

Page 7: PadhleBeta.net Aptitude Boats and Streams

Solution :

Let the speed of the boat in still water be x kmph. Then,

Speed downstream = (x + 3) kmph, Speed upstream = (x - 3)kmph.

(x + 3) * 1 = (x -3) * 3/2 2x + 6 = 3x - 9  x = 15 kmph.

PadhleBeta.net - Aptitude - Boats and Streams

9) Shiv takes twice as long to row a distance against the stream as to

row the same distance in favor of the stream. The ratio of the speed of

the boat(in still water) and the stream is:

1) 3:1 3) 1:3

2) 2:1 4) 1:1

Solution :

Let shiv’s rate upstream be x kmph. Then, his rate downstream =

2x kmph.

(Speed in still water) : (Speed of stream) 

= [2x + x / 2] : [2x - x / 2]

3x / 2 : x / 2 = 3:1.

PadhleBeta.net - Aptitude - Boats and Streams

10) Sachin rows to a place 48 km distance and back in 14 hours. He

finds that he can row 4 km with the stream in the same time as 3 km

against the stream. The rate of the stream is:

1) 1 km/hr 3) 1.5 km/hr

2) 10 km/hr 4) 5 km/hr

Page 8: PadhleBeta.net Aptitude Boats and Streams

Solution :

Suppose he moves 4 km downstream in x hours. Then,

Speed downstream = [4/x] km/hr, Speed upstream = [3/x] km/hr.

48/(4+x) + 48/(3/x) = 14 or x = 1/2.

So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

Rate of the stream = 1/2 (8-6) km/hr = 1 km/hr.

PadhleBeta.net - Aptitude - Boats and Streams

11) Sachin can row at 5 km/hr in still water. If the velocity of current is 1

km/hr and it takes him 1 hour to row to a place and come back, how far

is the place?

1) 1.2 km 3) 8 km

2) 2.4 km 4) 4 km

Solution :

Speed downstream = (5+1) kmph = 6 kmph;

Speed upstream = (5 - 1)kmph = 4 kmph.

Let the required distance be x km.

Then, x/6 + x/4 = 1 2x + 3x = 12 5x = 12  x = 2.4 km.

PadhleBeta.net - Aptitude - Boats and Streams

12) A boy can row 9 1/3 km/hr in still water and finds that it takes him

thrice a such time to row up than as to row down the same distance in

the river. The speed of the current is:

Page 9: PadhleBeta.net Aptitude Boats and Streams

1) 2 2/3  km/hr 3) 3 1/3  km/hr

2) 4 2/3  km/hr 4) 5 1/3  km/hr

Solution :

Let speed upstream be x kmph. Then, speed downstream = 3x kmph.

Speed in still water = 1/2(3x + x) kmph = 2x kmph.

2x = 28/3  x = 14/3

So, Speed upstream = 14/3 km/hr;

Speed downstream = 14/hr.

Hence, speed of the current = 1/2 [14 - 14/3] km/hr = 14/3 km/hr = 4 2/3

km/hr.

PadhleBeta.net - Aptitude - Boats and Streams

13) The speed of a boat in still water is 15 km/hr and the rate of current

is 3 km/hr the distance traveled downstream in 12 minutes is :

1) 1.4 km 3) 3.8 km

2) 1.2 km 4) 3.6 km

Solution :

Speed downstream = (15 + 3) kmph = 18 kmph.

Distance traveled = [18 * 12/60] km = 3.6 km.

PadhleBeta.net - Aptitude - Boats and Streams

14) Speed of a boat in standing water is 9 km/hr and the speed of the

stream is 1.5 km/hr. A boy rows to place at a distance of 105 km and

comes back to the starting point. The total time taken by him is:

Page 10: PadhleBeta.net Aptitude Boats and Streams

1) 12 hours 3) 15 hours

2) 21 hours 4) 24 hours

Solution :

Speed upstream = 7.5 kmph;

Speed downstream = 10.5 kmph.

total time taken = [105/7.5 + 105/10.5] hours = 24 hours.

PadhleBeta.net - Aptitude - Boats and Streams

15) A boat takes 19 hours for travelling downstream from point P to point

Q and coming back to a point R midway between P and Q. 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 P and Q?

1) 260 km 3) 180 km

2) 90 km 4) 120 km

Solution :

Speed downstream = (14 + 4) km/hr = 18 km/hr.

Speed upstream = (14 - 4) km/hr = 10 km/hr.

Let the distance between P and Q be x km. Then,

x/18 + (x/2)/10 = 19 x/18 + x/20 = 19 x = 180 km.