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Boats and Streams Problems and its Tricks

 Dear Readers,
As you know that All the basic Concepts of Time speed and Distance apply to this chapter Boats and streams.  We have to adjust the speeds according to the point whether the boat is moving against the stream or with the stream.

Stream: Moving water of the river is called stream.

Still Water: If the water is not moving then it is called still water.

Upstream: If a boat or a swimmer moves in the opposite direction of the stream then it is called upstream.


Downstream: If a boat or a swimmer moves in the same direction of the stream then it is called downstream.

Points to remember
  • When speed of boat or a swimmer is given then it normally means speed in still water.

Some Basic Formulas 
Rule 1: If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,

  • Speed of boat or swimmer upstream = (x − y) km/h
  • Speed of boat or swimmer downstream = (x + y) km/h
Rule 2:
  • Speed of boat or swimmer in still water is given by
  • Speed of stream is given by

Some Shortcut Methods
1: A man can row certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of stream is y km/h, then the speed of man in still water is given by
 


2: A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes him t hours to row to a place and come back, then the distance between two places is given by
3: A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance is given by
 

4: A man can row in still water at x km/h. In a stream flowing at y km/h, if he rows the same distance up and down the stream, then his average speed is given by
 


All types of Question asked in SSC Exams:- 

Type 1: A man rows a boat 18 kilometers in 4 hours downstream and return upstream in 12 hours.
The speed of the stream (in km per hour) is: (CGL-2003)
(a) 1                (b) 1.5
(c)2                 (d) 1.75         
Solution:
(b) Rate downstream  = 18/4=9/2 kmph
Rate upstream = 18/12=3/2 kmph.
Now, speed of the stream = (Rate downstream-Rate upstream)/2 = (9/2-3/2)/2=6/4=3/2=1.5 kmph.

Type2:A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. The speed of the boat in still water is: (CGL-2004)
(a) 6.5 km/hr.            (b) 5.5 km/hr.             
(c)6 km/hr.                (d) 5 km/hr.  
Solution
(b) Speed upstream =40/8=5 kmph
Speed downstream = 36/6 = 6 kmph
 Speed of boat in still water = 1/2 (5+6)=5.5 kmph

Type3: A boat goes 6 km an hour in still water, but takes thrice as much time in going the same distance against the current. The speed of the current (in km/hour) is: (CGL-2003)
(a) 4                            (b) 5   
(c)3                             (d) 2   
 Solution
(a)
 Let the speed of the current be x kmph.
According to the question,  6/(6-x)=3 
= 18 – 3x = 6
3x = 18 - 6
= x=12/3=4 kmph 

Type4: 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? (CGL-2004)
(a) 2.5 km                               
(b) 3 km          
(c)2.4 km                                
(d) 3.6 km     
Solution:
 (c) Let the distance be x km.
Speed upstream = 5 – 1= 4 kmph
Speed downstream = 5 + 1 = 6 kmph
x/6+x/4=4
(2x+3x)/12=1
5x = 12 = 1
x=12/5=2.4 km

Type5: Two boats A and B start towards each other from two places, 108 km apart. Speeds of the boats A and B in still water are 12km/hr proceeds down and B up the stream, they will meet after.                                                                                                                                                   (CGL-2008)
(a) 4.5 hours.                         
(b) 4 hours     
(c)5.4 hours               
(d) 6 hours   
Solution:
 (b) Let the speed of the stream be x kmph and both the boats meet after t hours
According o the question,
(12+x) (t-x) t=108 …(i)
12t + 15t = 108
27t = 108
 t = 108/27= 4 hours


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