aptitude : : boats and streams
 
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   Exercise 1
1.
The speed of Ramesh in still water be 12km|hr,find the speed of the stream?
 
A.
2.8km|hr

B.

1.9km|hr
C.
2.4km|hr
D.
1.4km|hr
   
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Answer: C
Explanation :
Speed of stream=(12(9-6))/(9+6)
                              =12(3)/15
                              =36/15
                              =2.4km|hr






 
2.
Ramesh can row a certain distance downstream in 6hours and return the same distance in 9hours.If the stream flows at the rate of 3km per hour,find the speed of Ramesh in still water?
 
A.
10km|hr

B.

12km|hr
C.
18km|hr
D.
15km|hr
   
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Answer: D
Explanation :
Ramesh's speed in still water=(3(9+6))/(9-6)
                                                     =(3*15)/3
                                                     =45/3
                                                     =15km|hr






 
3.
The current of a stream runs at the rate of 4km an hour. A boat goes 6km and back to the starting point in 2hours.The speed of the boat in still water is__________km/hr.
 
A.
8km|hr

B.

10km|hr
C.
4km|hr
D.
7km|hr
   
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Answer: A
Explanation :
Let the speed of boat in still water=xkm|hr
Speed of current=4km|hr
Speed of upstream=(x-4)km|hr
Speed downstream=(x+4)km|hr
 
Now,
   (6/(x-4))+(6/(x+4))=2
  or,
    (2x*2x)-32=6x+6x
    (x-8)(x+2)=0
 
    x=8 or x=-2
 
we reject the negative value.
 
Speed of boat in still water=8km|hr
 






 
4.
A man rows upstream 16km and downstream 28km,taking 5hours each time.The velocity of the current is_________km/hr.
 
A.
1.8km|hr

B.

1.2km|hr
C.
1.3km|hr
D.
1.9km|hr
   
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Answer: B
Explanation :
Upstream speed =16/5km|hr
Downstram speed=28/5km|hr
 
Velocity of current=((28/5)-(16/5))/2
                                =12/10
                                =1.2km|hr






 
5.
The speed of a boat in still water is 6km|hr and the speed of the stream is 1.5km|hr.A man rows to a place at a distance of 22.5km and comes back to the starting point.Find the total time taken by him.
 
A.
4hrs

B.

10hrs
C.
2hrs
D.
8hrs
   
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Answer: D
Explanation :
Boat's upstream speed=6-1.5=4.5km|hr
Boat's downstream speed=6+1.5=7.5km|hr
 
Total time=(22.5/4.5)+(22.5/7.5)=5.3=8hrs
 






 
6.
A man can row at 5km|hr in still water and the velocity of the current is 1km|hr.It takes him 1hour to row to a place and back.How far is the place?
 
A.
2.4km

B.

3.2km
C.
2.7km
D.
5.4km
   
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Answer: A
Explanation :
Distance=(1*{52-12})/(2*5)
                =24/10
                =2.4km
 






 
7.
A boat travels upstream from B to A and downstream from A to B in 3hours.If the speed of the boat in still water is 9km|hr and the speed of the current is 3km|hr,the distance between A and B is__________km.
 
A.
10km

B.

5km
C.
8km
D.
12km
   
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Answer: D
Explanation :
Let the distance be X km.
 
Now,upstream speed=9-3=6km|hr  
         downstream speed=9+3=12km|hr
 
Total time taken in upstream  and downstream journey
 
                         =(X/6)+(X/12)=3 or (18X/72) =3
                       
                       X=(3*72)/18=12km
 
Short Cut:
Distance= Total time {(speed in still water)2-(speed of current)2}/(2X speed in still water)
 






 
8.
A boat goes 40 km upstream in 8hours and 36km downstream in 6hours.The speed of the boat in still water is_____km|hr.
 
A.
1.5km|hr

B.

5.5km|hr
C.
7.5km|hr
D.
3.5km|hr
   
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Answer: B
Explanation :
                                           
Boat's upstream speed = 40/8=5km|hr
                                                   
Boat's downstream speed = 36/6=6km|hr.
 
Speed of boat in still water=(5+6)/2=5.5km|hr
 






 
9.
If a man's rate with the current is I2km|hr and the rate of the current is 1.5km|hr,then the man's rate against the current is_______km/hr.
 
A.
9km|hr

B.

12km|hr
C.
5km|hr
D.
2km|hr
   
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Answer: A
Explanation :
Man's rate with the current= 12km|hr.
 
Man's rate in still water= 12-1.5 
                                         = 10.5km|hr 
 
Man's rate against current= 10.5-1.5 
                                               = 9km|hr
 






 
10.
A boat covers 24km upstream and 36km downstream in 6hours,while it covers 36km upstream and 24km downstream in 6.5hrs.Find the velocity of the current?
 
A.
3km|hr

B.

7km|hr
C.
10km|hr
D.
2km|hr
   
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Answer: D
Explanation :
US   OS   Time
24     36     6
 
36     24     6.5
 
Upstream speed of boat = ((24*24)-(36*3))/((24*6)-(36*6.5))
                                            = 720/(-90)
                                            = 8km|hr
Downstream speed of boat = ((24*24)-(36*36))/((24*6.5)-(36*6))
                                                  = 720/(-60)
                                                  =12km|hr
Speed of current=(12-8)/2
                              =2km|hr






 

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