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Boats and Streams - General Questions (1)

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  • Boats and Streams - General Questions
1. 

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. 1.5 km/hr
C. 2 km/hr
D. 2.5 km/hr

Answer: Option A

Explanation:

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

Speed downstream = 1-sym-oparen-h1 4 1-sym-cparen-h1 km/hr.
x
Speed upstream = 1-sym-oparen-h1 3 1-sym-cparen-h1 km/hr.
x
48 + 48 = 14 or x = 1 .
(4/x) (3/x) 2

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

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

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:

A. 2 : 1
B. 3 : 1
C. 3 : 2
D. 4 : 3

Answer: Option B

Explanation:

Let man's rate upstream be x kmph.

Then, his rate downstream = 2x kmph.

 (Speed in still water) : (Speed of stream) = 1-sym-oparen-h1 2x + x 1-sym-cparen-h1 : 1-sym-oparen-h1 2x - x 1-sym-cparen-h1
2 2
   = 3x : x
2 2

   = 3 : 1.

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3. 

Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

A. 16 hours
B. 18 hours
C. 20 hours
D. 24 hours

Answer: Option D

Explanation:

Speed upstream = 7.5 kmph.

Speed downstream = 10.5 kmph.

 Total time taken = 1-sym-oparen-h1 105 + 105 1-sym-cparen-h1hours = 24 hours.
7.5 10.5
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4. 

A man can row three-quarters of a kilometre against the stream in 11 1-div-1by4 minutes and down the stream in 7 1-div-1by2 minutes. The speed (in km/hr) of the man in still water is:

A. 2
B. 3
C. 4
D. 5

Answer: Option D

Explanation:

We can write three-quarters of a kilometre as 750 metres,

and 111-div-1by4 minutes as 675 seconds.

Rate upstream = 1-sym-oparen-h1 750 1-sym-cparen-h1m/sec = 10 m/sec.
675 9
Rate downstream = 1-sym-oparen-h1 750 1-sym-cparen-h1m/sec = 5 m/sec.
450 3
 Rate in still water = 1 1-sym-oparen-h1 10 + 5 1-sym-cparen-h1m/sec
2 9 3
   = 25 m/sec
18
   = 1-sym-oparen-h1 25 x 18 1-sym-cparen-h1km/hr
18 5

   = 5 km/hr.

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5. 

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. 40 minutes
B. 1 hour
C. 1 hr 15 min
D. 1 hr 30 min

Answer: Option C

Explanation:

Rate downstream = 1-sym-oparen-h1 1 x 60 1-sym-cparen-h1km/hr = 6 km/hr.
10

Rate upstream = 2 km/hr.

Speed in still water = 1 (6 + 2) km/hr = 4 km/hr.
2
 Required time = 1-sym-oparen-h1 5 1-sym-cparen-h1hrs = 1 1 hrs = 1 hr 15 min.
4 4
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6. 

A boat covers a certain distance downstream in 1 hour, while it comes back in 1 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

A. 12 kmph
B. 13 kmph
C. 14 kmph
D. 15 kmph
E. None of these

Answer: Option D

Explanation:

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) x 1 = (x - 3) x 3
2

 2x + 6 = 3x - 9

 x = 15 kmph.

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7. 

A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

A. 2.4 km
B. 2.5 km
C. 3 km
D. 3.6 km

Answer: Option A

Explanation:

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

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

Let the required distance be x km.

Then, x + x = 1
6 4

 2x + 3x = 12

 5x = 12

 x = 2.4 km.

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8. 

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

A. 2 mph
B. 2.5 mph
C. 3 mph
D. 4 mph

Answer: Option A

Explanation:

Let the speed of the stream x mph. Then,

Speed downstream = (10 + x) mph,

Speed upstream = (10 - x) mph.

36 - 36 = 90
(10 - x) (10 + x) 60

 72x x 60 = 90 (100 - x2)

 x2 + 48x - 100 = 0

 (x+ 50)(x - 2) = 0

 x = 2 mph.

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