Boats and Streams Problems and Solutions

• 1. In one hour, a boat goes 11km along the stream and 5 km against it. Find the speed of the boat in still water

  1. 6
  2. 7
  3. 8
  4. 9

  Answer :

  Option C

  Explanation:

  We know we can calculate it by 1/2(a+b)
  
  => 1/2(11+5) = 1/2(16) = 8 km/hr

• 2. If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is

  1. 5 km/hr
  2. 4 km/hr
  3. 2 km/hr
  4. 1 km/hr

  Answer :

  Option D

  Explanation:

  Rate upstream = (15/3) kmph
  Rate downstream (21/3) kmph = 7 kmph.
  Speed of stream (1/2)(7 - 5)kmph = 1 kmph

• 3. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is

  1. 2 km/hr
  2. 3 km/hr
  3. 4 km/hr
  4. 5 km/hr

  Answer :

  Option D

  Explanation:

  Let the speed of the stream be x km/hr. Then,
  Speed downstream = (15 + x) km/hr,
  Speed upstream = (15 - x) km/hr
  
  So we know from question that it took 4(1/2)hrs to travel back to same point.
  
  So,
  \begin{aligned}
  \frac{30}{15+x} - \frac{30}{15-x} = 4\frac{1}{2} \\
  => \frac{900}{225 - x^2} = \frac{9}{2} \\
  => 9x^2 = 225 \\
  => x = 5 km/hr
  \end{aligned}

• 4. A man can row \begin{aligned} 9\frac{1}{3} \end{aligned} 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.

  1. \begin{aligned} 3\frac{2}{3}kmph \end{aligned}
  2. \begin{aligned} 4\frac{2}{3}kmph \end{aligned}
  3. \begin{aligned} 5\frac{2}{3}kmph \end{aligned}
  4. \begin{aligned} 6\frac{2}{3}kmph \end{aligned}

  Answer :

  Option B

  Explanation:

  Friends first we should analyse quickly that what we need to calculate and what values we require to get it.
  
  So here we need to get speed of current, for that we will need speed downstream and speed upstream, because we know
  Speed of current = 1/2(a-b) [important]
  
  Let the speed upstream = x kmph
  Then speed downstream is = 3x kmph [as per question]
  
  \begin{aligned}
  \text{speed in still water = } \frac{1}{2}(a+b) \\
  => \frac{1}{2}(3x+x) \\
  => 2x \\
  \text{ as per question we know, }\\
  2x = 9\frac{1}{3} \\
  => 2x = \frac{28}{3} => x = \frac{14}{3} \\
  \end{aligned}
  So,
  Speed upstream = 14/3 km/hr, Speed downstream 14 km/hr.
  Speed of the current \begin{aligned} =\frac{1}{2}[14 - \frac{14}{3}]\\
  = \frac{14}{3}
  = 4 \frac{2}{3} kmph \end{aligned}

• 5. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is

  1. 1.6 km
  2. 2 km
  3. 3.6 km
  4. 4 km

  Answer :

  Option C

  Explanation:

  Speed downstreams =(15 + 3)kmph
  = 18 kmph.
  Distance travelled = (18 x 12/60)km
  = 3.6km

• 6. A man's speed with the current is 20 kmph and speed of the current is 3 kmph. The Man's speed against the current will be

  1. 11 kmph
  2. 12 kmph
  3. 14 kmph
  4. 17 kmph

  Answer :

  Option C

  Explanation:

  If you solved this question yourself, then trust me you have a all very clear with the basics of this chapter.
  
  If not then lets solve this together.
  
  Speed with current is 20,
  speed of the man + It is speed of the current
  Speed in still water = 20 - 3 = 17
  
  Now speed against the current will be
  speed of the man - speed of the current
  = 17 - 3 = 14 kmph

• 7. A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.

  1. .4 km
  2. 1.4 km
  3. 2.4 km
  4. 3.4 km
  5. Only argument I is strong
  6. Only argument II is strong
  7. Either I or II is strong
  8. Neither I nor II is strong
  9. Both I and II are strong

  Answer :

  Option F

  Explanation:

  Let the distance is x km
  Rate downstream = 5 + 1 = 6 kmph
  Rate upstream = 5 - 1 = 4 kmph
  then
  x/6 + x/4 = 1 [because distance/speed = time]
  => 2x + 3x = 12
  => x = 12/5 = 2.4 km