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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)/*2*y*km

- A man rows a certain distance downstream in t
_{1}hours and returns the same distance upstream in t_{2}hours. If the speed of the stream is y km/hr, then the speed of the man in still water

=*y(*(*t*2+*t*1)*/*(*t*2−*t*1)) 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*))/2*x*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__

1. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is: | |

A. 8.5 km/hr | B. 10 km/hr. |

C. 12.5 km/hr | D. 9 km/hr |

** 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

2. In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is: | |

A. 12 km/hr | B. 11 km/hr |

C. 10 km/hr | D. 8 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.

3. A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water? | |

A. 2 hr 30 min | B. 2 hr |

C. 4 hr | D. 1 hr 15 min |

**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

4. Speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph. A man rows to a place at a distance of 4864 km and comes back to the starting point. The total time taken by him is: | |

A. 700 hours | B. 350 hours |

C. 1400 hours | D. 1010 hours |

**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

5. The speed of a boat in still water in 22 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is: | |

A. 9.4 km | B. 10.2 km |

C. 10.4 km | D. 9.2 km |

**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

6. A boat covers a certain distance downstream in 1 hour, while it comes back in 1 | |

A. 14 kmph | B. 15 kmph |

C. 13 kmph | D. 12 kmph |

**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 1^{1}⁄_{2} hour.

ie, distance travelled downstream in 1 hour = distance travelled upstream in 1^{1}⁄_{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

7. A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 54 km downstream | |

A. 5 hours | B. 4 hours |

C. 3 hours | D. 2 hours |

**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

8. A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water? | |

A. 5 kmph | B. 4.95 kmph |

C. 4.75 kmph | D. 4.65 |

**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

9. A man takes twice as long to row a distance against the stream as to row the same distance in favor of the stream. The ratio of the speed of the boat (in still water) and the stream is: | |

A. 3 : 1 | B. 1 : 3 |

C. 1 : 2 | D. 2 : 1 |

**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

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