2. Boat and Stream, Quantitative Aptitude, Civil Service Examination, RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan) PDF Download

Boat and stream problems is a sub-set of time, speed and distance type questions where in relative speed takes the foremost role. We always find several questions related to the above concept in SSC common graduate level exam as well as in bank PO exam. Upon listing the brief theory of the issue below we move to the various kinds of problems asked in the competitive examination.

Important Formulas - Boats and Streams

• Downstream
  In running/moving water, the direction along the stream is called downstream.
• Upstream
  In running/moving water, the direction against the stream is called upstream.
• Let the speed of a boat in still water be u km/hr and the speed of the stream be v km/hr, then
  
  Speed downstream = (u+v) km/hr
  Speed upstream = (u - v) km/hr
   
• Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
  
  Speed in still water =1/2*(a+b)km/hr
  Rate of  stream = 1/2*(a−b) km/hr

Some more short-cut methods

• Assume that a man can row at the speed of x km/hr in still water and he rows the same distance up and down in a stream which flows at a rate of y km/hr. Then his average speed throughout the journey
  
  = (Speed downstream × Speed upstream)/Speed in still water=((x+y)(x−y))/x km/hr
   
• Let the speed of a man in still water be x km/hr and the speed of a stream be y km/hr. If he takes t hours more in upstream than to go downstream for the same distance, the distance
  
  = ((x* x –y* y)*t)/2y km
   
• A man rows a certain distance downstream in t₁ hours and returns the same distance upstream in t₂ hours. If the speed of the stream is y km/hr, then the speed of the man in still water
  
  =y((t2+t1) / (t2−t1)) km/hr
   
• A man can row a boat in still water at x km/hr. In a stream flowing at y km/hr, if it takes him t hours to row a place and come back, then the distance between the two places
  
  =t((x* x –y* y))/2x km
• A man takes n times as long to row upstream as to row downstream the river. If the speed of the man is x km/hr and the speed of the stream is y km/hr, then
  
  x=y*((n+1)/(n−1))

Solved Examples
 

 
Answer : Option B

Explanation :

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

Answer : Option B

Explanation :

Let the speed downstream be a km/hr and the speed upstream be b km/hr, then

Speed in still water =1/2(a+b) km/hr and Rate of stream =1/2(a−b) km/hr
Speed in still water = 1/2(14+8) kmph = 11 kmph.

Answer : Option A

Explanation :

Speed upstream = 2/2=1 km/hr

Speed downstream = 1/(20/60)=3 km/hr

Speed in still water = 1/2(3+1)=2 km/hr

Time taken to travel 5 km in still water = 5/2= 2 hour 30 minutes

Answer : Option A

Explanation :

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

Answer : Option C

Explanation :

Speed downstream = (22 + 4) = 26 kmph

Time = 24 minutes = 24/60 hour = 2/5 hour

distance travelled = Time × speed = (2/5)×26 = 10.4 km

Answer : Option B

Explanation :

Let the speed of the boat in still water = x kmph

Given that speed of the stream = 3 kmph

Speed downstream = (x+3) kmph

Speed upstream = (x-3) kmph

He 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 hour

since 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

Answer : Option D

Explanation :

Speed of the boat in still water = 22 km/hr

speed of the stream = 5 km/hr

Speed downstream = (22+5) = 27 km/hr

Distance travelled downstream = 54 km

Time taken = distance/speed=54/27 = 2 hours

Answer : Option B

Explanation :

Speed downstream = 22/4 = 5.5 kmph

Speed upstream = 22/5 = 4.4 kmph

Speed of the boat in still water = (½) x (5.5+4.42) = 4.95 kmph

Answer : Option A

Explanation :

Let speed upstream = x

Then, speed downstream = 2x

Speed in still water = (2x+x)2=3x/2

Speed of the stream = (2x−x)2=x/2

Speed of boat in still water: Speed of the stream = 3x/2:x/2 = 3 : 1