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Boat And Stream - MCQ Test(1) - UPSC MCQ


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16 Questions MCQ Test - Boat And Stream - MCQ Test(1)

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Boat And Stream - MCQ Test(1) - Question 1
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A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:

Detailed Solution for Boat And Stream - MCQ Test(1) - Question 1

Option B

Explanation :Man's speed with the current = 15 km/hr=>speed of the man + speed of the current = 15 km/hrspeed of the current is 2.5 km/hrHence, speed of the man = 15 ‐ 2.5 = 12.5 km/hrman's speed against the current = speed of the man ‐ speed of the current= 12.5 ‐ 2.5 = 10 km/hr

Boat And Stream - MCQ Test(1) - Question 2
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In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed ofthe boat in still water (in km/hr) is:

Detailed Solution for Boat And Stream - MCQ Test(1) - Question 2

Option B

Explanation :Let the speed downstream be a km/hr and the speed upstream be b km/hr, thenSpeed in still water =1/2(a+b) km/hr and Rate of stream =1/2(a−b) km/hrSpeed in still water = 1/2(14+8) kmph = 11 kmph.

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Boat And Stream - MCQ Test(1) - Question 3
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A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the currentin 20 minutes. How long will it take to go 5 km in stationary water?

Detailed Solution for Boat And Stream - MCQ Test(1) - Question 3

Option A

Explanation :Speed upstream = 2/2=1 km/hrSpeed downstream = 1/(20/60)=3 km/hrSpeed in still water = 1/2(3+1)=2 km/hrTime taken to travel 5 km in still water = 5/2= 2 hour 30 minutes

Boat And Stream - MCQ Test(1) - Question 4
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Speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph. A manrows to a place at a distance of 4864 km and comes back to the starting point. The total time taken by him is:
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 4

Speed downstream = (14 + 1.2) = 15.2 kmph

Speed upstream = (14 ‐ 1.2) = 12.8 kmph

Total time taken = 4864/15.2+4864/12.8 = 320 + 380 = 700 hours

Boat And Stream - MCQ Test(1) - Question 5
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 A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 5

Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr

speed of the current is 2.5 km/hr
Hence, speed of the man = 15 - 2.5 = 12.5 km/hr

man's speed against the current = speed of the man - speed of the current
= 12.5 - 2.5 = 10 km/hr

Boat And Stream - MCQ Test(1) - Question 6
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A boat covers a certain distance downstream in 1 hour, while it comes back in 11⁄2 hours. If thespeed of the stream be 3 kmph, what is the speed of the boat in still water?
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 6

Option B

Explanation :Let the speed of the boat in still water = x kmphGiven that speed of the stream = 3 kmphSpeed downstream = (x+3) kmphSpeed upstream = (x‐3) kmphHe travels a certain distance downstream in 1 hour and come back in 11⁄2 hour.ie, distance travelled downstream in 1 hour = distance travelled upstream in 11⁄2 hoursince distance = speed × time, we have(x+3)×1=(x−3)*3/2=> 2(x + 3) = 3(x‐3)=> 2x + 6 = 3x ‐ 9=> x = 6+9 = 15 kmph

Boat And Stream - MCQ Test(1) - Question 7
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A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 54 km downstream
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 7

Option D

Explanation :Speed of the boat in still water = 22 km/hrspeed of the stream = 5 km/hrSpeed downstream = (22+5) = 27 km/hrDistance travelled downstream = 54 kmTime taken = distance/speed=54/27 = 2 hours

Boat And Stream - MCQ Test(1) - Question 8
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A boat running downstream covers a distance of 22 km in 4 hours while for covering the samedistance upstream, it takes 5 hours. What is the speed of the boat in still water?
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 8

Option B

Explanation :Speed downstream = 22/4 = 5.5 kmphSpeed upstream = 22/5 = 4.4 kmphSpeed of the boat in still water = (½) x (5.5+4.42) = 4.95 kmph

Boat And Stream - MCQ Test(1) - Question 9
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A man takes twice as long to row a distance against the stream as to row the same distance infavor of the stream. The ratio of the speed of the boat (in still water) and the stream is:
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 9

Option A

Explanation :Let speed upstream = xThen, speed downstream = 2xSpeed in still water = (2x+x)2=3x/2Speed of the stream = (2x−x)2=x/2Speed of boat in still water: Speed of the stream = 3x/2:x/2 = 3 : 1

Boat And Stream - MCQ Test(1) - Question 10
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A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in atotal of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 10

Option C

Explanation :Speed of the motor boat = 15 km/hr

Let speed of the stream = v

Speed downstream = (15+v) km/hrSpeed upstream = (15‐v) km/hr

Time taken downstream = 30/(15+v)

Time taken upstream = 30/(15−v)

total time = 30/(15+v)+30/(15−v)

It is given that total time is 4 hours 30 minutes = 4.5 hour = 9/2 hour

i.e.,30/(15+v)+30/(15−v)=9/2⇒

1(15+v)+1(15−v)=(9/2)×30=3/20

⇒(15−v+15+v)/(15+v)(15−v)=3/20

⇒30/(15*15−v*v)=3/20

⇒30/(225−v*v)=3/20

⇒10/(225−v* v)=1/20

⇒225−v* v =200

⇒v* v =225−200=25

⇒v=5 km/hr

Boat And Stream - MCQ Test(1) - Question 11
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A man rows to a place 48 km distant and come 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:

A. 1 km/hr. B. 2 km/hr.

C. 1.5 km/hr. D. 2.5 km/hr
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 11

Option A

Explanation :Assume that he moves 4 km downstream in x hours

Then, speed downstream = distance/time=4/x km/hrGiven that he can row 4 km with the stream in the same time as 3 km against the stream

i.e., speed upstream = 3/4of speed downstream=> speed upstream = 3/x km/hr

He rows to a place 48 km distant and come back in 14 hours

=>48/(4/x)+48/(3/x)=14

==>12x+16x=14

=>6x+8x=7=>14x=7

=>x=1/2

Hence, speed downstream = 4/x=4/(1/2) = 8 km/hr

speed upstream = 3/x=3/(1/2) = 6 km/hr

Now we can use the below formula to find the rate of the stream

Let the speed downstream be a km/hr and the speed upstream be b km/hr, thenSpeed in still water =1/2*(a+b) km/hr

Rate of stream =12*(a−b) km/hr

Hence, rate of the stream = ½*(8−6)=1 km/hr

Boat And Stream - MCQ Test(1) - Question 12
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A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4hours to cover the same distance running downstream. What is the ratio between the speed of theboat and speed of the water current respectively?
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 12

Option C

Explanation :Let the rate upstream of the boat = x kmphand the rate downstream of the boat = y kmph

Distance travelled upstream in 8 hrs 48 min = Distance travelled downstream in 4 hrs.Since distance = speed × time, we havex×(8*4/5)=y×4x×(44/5)=y×4x×(11/5)=y‐‐‐ (equation 1)

Now consider the formula given belowLet the speed downstream be a km/hr and the speed upstream be b km/hr, thenSpeed in still water =1/2(a+b) km/hr

Rate of stream =1/2(a−b) km/hrHence, speed of the boat = (y+x)/2speed of the water = (y−x)/2Required Ratio = (y+x)/2:(y−x)/2=(y+x):(y−x)=(11x/5+x):(11x/5−x)(Substituted the value of y from equation 1)= (11x+5x):(11x−5x)=16x:6x=8:3

Boat And Stream - MCQ Test(1) - Question 13
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. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hourto row to a place and come back, how far is the place?
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 13

Option C

Explanation :Speed in still water = 5 kmphSpeed of the current = 1 kmphSpeed downstream = (5+1) = 6 kmphSpeed upstream = (5‐1) = 4 kmphLet the requited distance be x kmTotal time taken = 1 hour=>x/6+x/4=1=> 2x + 3x = 12=> 5x = 12=> x = 2.4 km

Boat And Stream - MCQ Test(1) - Question 14
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A man can row three‐quarters of a kilometer against the stream in 111⁄4 minutes and down thestream in 71⁄2 minutes. The speed (in km/hr) of the man in still water is:
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 14

Option B

Explanation :Distance = 3/4 kmTime taken to travel upstream = 111⁄4 minutes= 45/4 minutes = 45/(4×60) hours = 3/16 hoursSpeed upstream = Distance/Time= (3/4)/ (3/16) = 4 km/hrTime taken to travel downstream = 71⁄2minutes = 15/2 minutes = 15/2×60 hours = 1/8 hoursSpeed downstream = Distance/Time= (3/4)/ (1/8) = 6 km/hrRate in still water = (6+4)/2=10/2=5 kmph

Boat And Stream - MCQ Test(1) - Question 15
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A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distanceupstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 15

Option D

Explanation :Speed of the boat in still water = 10 mphLet speed of the stream be x mphThen, speed downstream = (10+x) mphspeed upstream = (10‐x) mphTime taken to travel 36 miles upstream ‐ Time taken to travel 36 miles downstream= 90/60 hours=>36/(10−x)−36/(10+x)=3/2 =>12/(10−x)−12/(10+x)=1/2 =>24(10+x)−24(10−x)=(10+x)(10−x)=>240+24x−240+24x=(100−x* x) =>48x=100− (x* x) => x* x +48x−100=0=>(x+50)(x−2)=0 =>x = ‐50 or 2; Since x cannot be negative, x = 2 mph

Boat And Stream - MCQ Test(1) - Question 16
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At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours lessthan it takes him to travel the same distance upstream. But if he could double his usual rowing ratefor his 24‐mile round trip, the downstream 12 miles would then take only one hour less than theupstream 12 miles. What is the speed of the current in miles per hour?
Detailed Solution for Boat And Stream - MCQ Test(1) - Question 16

Option D

Explanation :Let the speed of Rahul in still water be x mphand the speed of the current be y mphThen, Speed upstream = (x ‐ y) mphSpeed downstream = (x + y) mphDistance = 12 milesTime taken to travel upstream ‐ Time taken to travel downstream = 6 hours⇒12/(x−y)−12/(x+y)=6⇒12(x+y)−12(x−y)=6(x*x−y*y)⇒24y=6(x*x−y*y)⇒4y= x*x−y*y⇒x * x =(y* y +4y)⋯(Equation 1)Now he doubles his speed. i.e., his new speed = 2xNow, Speed upstream = (2x ‐ y) mphSpeed downstream = (2x + y) mphIn this case, Time taken to travel upstream ‐ Time taken to travel downstream = 1 hour⇒12/(2x−y)−12/(2x+y)=1⇒12(2x+y)−12(2x−y)=4*x* x –y* y⇒24y=4*x* x –y* y⇒4*x* x = y* y +24y⋯(Equation 2)(Equation 1 × 4)⇒4x* x =4(y* y +4y)⋯(Equation 3)(From Equation 2 and 3, we have)y* y +24y=4(y* y +4y) ⇒y* y +24y=4y* y +16y ⇒3y* y =8y ⇒3y=8y=8/3 mph i.e., speed of the current = 8/3 mph=2*2/3 mph

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