Boats and Streams

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.


1. The upstream and downstream speeds of a boat are 7 kmph and 11 kmph respectively. Find the speed of the boat.

A. 9 m/s

B. 5 m/s

C. 2 m/s

D. 2.5 m/s


Answer

                  Ans: Option D

       Explanation:

       Let,

       Upstream speed as u

       Downstream speed as d

       Speed of the boat as b

       so,b = (u+d)/2 = 9 kmph ,

       The options are given in m/s. 9 kmph = (9*5/18) m/s = 2.5 m/s 


2. A man can row downstream at 14 km/hr and upstream at 9 km/hr. Man’s rate in still water is :

A. 5 km/hr

B. 23 km/hr

C. 11.5 km/hr

D. none of these


Answer

                  Ans: Option C

       Explanation:

       No explanation 


3. In one hour, a boat travels 9 km upstream. It takes the same time to travel 15 km downstream. Find the speed of the stream.

A. 2.5 kmph

B. 3 kmph

C. 2 kmph

D. 4 kmph


Answer

                  Ans: Option B

       Explanation:

       Let,

       Upstream speed as u

       Downstream speed as d

       u=9kmph,d=15kmph,

        s=(d-u)/2 =(15-9)/2= 3kmph


4. A man rows 20km upstream in 150 minutes. If the speed of the stream is 4.5 kmph, find his speed in still water.

A. 12.5 kmph

B. 8 kmph

C. 3.5 kmph

D. 7.5 kmph


Answer

                  Ans: Option A

       Explanation:

       150 mins=2.5 hrs

       Upstream speed =distance/time= 20/2.5 = 8 kmph

       Speed in still water = 8+4.5 = 12.5 kmph 


5. A man swims a distance of 35 km against the current in 5 hours and a distance of 39 km downstream in 3 hours. Find the time taken by him to cover a distance of 40 km in still water.

A. 3.5 hours

B. 3.9 hours

C. 4.5 hours

D. 4 hours


Answer

                  Ans: Option D

       Explanation:

       u = 35/5 = 7 kmph

       d = 39/3 = 13 kmph ,

       The man's speed = u+d/2 = 10 kmph

       He can cover a distance of 40 km in = 40/10 = 4 hours 


6. A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9 km/hr and the speed of the current is 3 km/hr, the distance between A and B is :

A. 4 km

B. 6 km

C. 8 km

D. 12 km


Answer

                  Ans: Option D

       Explanation:

       No explanation 


7. A boatman starts from point A at 11:00 am and travels downstream to point B, stays there for an hour and returns to point A at 4:00 pm. If the speed of the boat and stream are 12 km/hr and 3 km/hr respectively, find the distance between A and B.

A. 45 km

B. 22.5 km

C. 36 km

D. 27 km


Answer

                  Ans: Option D

       Explanation:

       Upstream and downstream travel took him 4 hours (leaving his 1 hour stay at B).

       u = 9 km/hr ,d = 15 km/hr

       so the distance between A and B=>(x/9) + (x/15) = 4

       Distance = 22.5 km 


8. A boat takes 38 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 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?

A. 240 km

B. 120 km

C. 360 km

D. 180 km


Answer

                  Ans: Option C

       Explanation:

      Velocity of the stream = 4 kmph

      Speed of the boat in still water is 14 kmph

      Speed downstream = (14+4) = 18 kmph

      Speed upstream = (14-4) = 10 kmph

      Let the distance between A and B be x km

      Time taken to travel downstream from A to B + Time taken to travel upstream from B to C(mid of A and B)= 38 hours

      (x/18)+(x2)/10=38

      (x/18)+(x2/10)=38

      19x/180=38

      x/180=2

     x=360i.e., the distance between A and B = 360 km


9. A man can row 9 and 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. The speed of the current is .

A. 3 and 1/3 km/hr

B. 4 and 2/3 km/hr

C. 3 and 1/9 km/hr

D. 14 km/hr


Answer

                  Ans: Option B

       Explanation:

       Let speed upstream is x kmph.

       Then, speed downstream = 3x kmph.

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

        2x = 28/3 x

        = 14/3

       Speed upstream = 14/3 km/hr, Speed downstream 14 km/hr.

      Speed of the current = (1/2)[14 – (14/3)] = 14/3 = 4 and 2/3 kmph 


10. The current of a stream runs at 1 km/hr. A motor boat goes 35 km upstream and back again to the starting point in 12 hours. The speed of motorboat in still water is :

A. 6 km/hr

B. 7 km/hr

C. 8.5 km/hr

D. 8 km/hr


Answer

                  Ans: Option A

       Explanation:

       No explanation 


11. The time taken by a ship to travel 48 km downstream is equal to the time taken to travel 32 km upstream. If the velocity of the stream is 4 kmph, find the speed of the ship.

A. 16 kmph

B. 20 kmph

C. 18 kmph

D. 24 kmph


Answer

                  Ans: Option B

       Explanation:

       No explanation 


12. A man can swim 3 km/hr in still water. If the velocity of the stream be 2 km/hr, the time taken by him to swim to place 10 km upstream and back, is :

A. 8 hrs

B. 16 hrs

C. 10 hrs

D. 12 hrs


Answer

                  Ans: Option D

       Explanation:

       No explanation 


13. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

 A.4 km/hr

B.6 km/hr

C. 8 km/hr

D. Data inadequate


Answer

                  Ans: Option B

       Explanation:

       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. 


14. Find the ratio between the speeds of the boat and stream if the boat can travel 30 km upstream in 3 hours and the same distance downstream in 2 hours.

A. 5:1

B. 3:2

C. 4:1

D. 2


Answer

                  Ans: Option A

       Explanation:

       Let

       upstream speed u = 10 kmph

       Downstream speed d = 15 kmph

       Speed of the stream s = (d-u)/2 = 2.5 kmph

       Speed of the boat b = (d+u)/2 = 12.5 kmph

        b:s = 5:1 


15. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 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?

A. 2 : 1

B. 3 : 2

C. 8 : 3

D. Cannot be determined

E. None of these 


Answer

                  Ans: Option C

       Explanation:

      Let the man's rate upstream be x kmph and that downstream be y kmph.

      Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

      ( x x 44/5)   = (y x 4) 

      (44/5) x =4y

       y = 11/5 x.

      Required ratio =   (y + x)/2   :   (y – x)/2 

     =   (16x/5)  x (1/2)   :   (6x/5)x (1/2) 

     = (8/5) : (3/5)

     =8:3


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