Quantitative Aptitude

Boats and Streams

369 Questions
All Recover still-water and stream speeds 136 Calculate one-way and round-trip time 61 Ratio of boat to stream speed 54 Use time differences and equal-distance ratios 39 Perpendicular river crossing 36 Round-trip average speed 14 Angles of drift 12 Handle drifting objects 8 Solve meeting and separation problems 6 Fixed-time distance ratios 3

Boats and Streams Questions

Multiple choice

Two persons P and Q crosses the river starting from point A to exactly opposite point B on the other bank of the river. The person P crosses the river in the shortest path. The person Q crosses the river in the shortest time and walks back to point B. Velocity of river is $3kmph$ and speed of each boat is $5kmph$ w.r.t. water. If the two persons reach the point B in the same time, then the speed of walk of Q is
  1. $5kmph$
  2. $12kmph$
  3. $20kmph$
  4. $25kmph$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

A boat is to cross a river of width 500 m. The velocity of the river flow is 5 kmph and the velocity of the boat is 10 krnph. The angle at which the boat is to be rowed with the direction of river flow velocity so that the boat can cross the river along shortest path is
  1. $120^o$
  2. $135^o$
  3. $150^o$
  4. $60^o$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the shortest crossing path, the resultant velocity must be perpendicular to the river flow. The boat's upstream velocity component must therefore cancel the river velocity, so 10 cos(theta) + 5 = 0. Hence cos(theta) = -1/2 and theta = 120 degrees.

Multiple choice

A boat which is rowed with constant velocity u, starts from point A on the bank of river which flows with a constant velocity v and its points always towards a point B. On the other bank exactly opposite to A, the equation of the path of boat is:
  1. $r\sin \theta =c\left(\tan \dfrac{\theta}{2}\right)^{u/v}$
  2. $r\sin\theta =\dfrac{u}{v}$
  3. $r^2\sin\theta =\dfrac{u}{v}$
  4. $ur^2=v\sin^2\theta$

  5. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a classic pursuit problem. The path of a boat moving towards a target moving at a constant velocity is described by a specific differential equation, which leads to the solution r * sin(theta) = c * (tan(theta/2))^(u/v).

Multiple choice

A man can row a boat with $4 km/h$ in still water. If he is crossing a river where the current is $2 km/h$. Width of river is $4 km$. In what direction should he head the boat if he wants to cross the river in shortest time and what is this minimum time?
  1. Parallel to river current, $2$ hrs
  2. Perpendicular to river current, $2$ hrs
  3. Parallel to river current, $1$ hrs
  4. Perpendicular to river current, $1$ hrs
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To cross in the shortest time, the boat must head perpendicular to the current. The velocity component across the river is 4 km/h. Time = Distance / Velocity = 4 km / 4 km/h = 1 hour.

Multiple choice

A steamer moves with velocity 3 km/h in and against the direction of river water whose velocity is 2 km/h. Calculate the total time for the total journey if the boat travels 2 km in the direction of a stream and then back to its place:

  1. 2 hrs

  2. 2.5 hrs

  3. 2.4 hrs

  4. 3 hrs.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = 3 + 2 = 5 km/h. Upstream speed = 3 - 2 = 1 km/h. Time downstream = 2 / 5 = 0.4 hours. Time upstream = 2 / 1 = 2 hours. Total time = 0.4 + 2 = 2.4 hours.

Multiple choice

A boat takes $7$ hours to travel $30km$ upstream and $28km$ downstairs. It takes $5$ hours to travel $21km$ upstream and to return back. Find the speed of the boat in still water.
  1. $10$ $km/hr$
  2. $20$ $km/hr$
  3. $14$ $km/hr$
  4. $6$ $km/hr$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the upstream and downstream speeds be u and d. From 21/u + 21/d = 5 and 30/u + 28/d = 7, we obtain u = 6 km/hr and d = 14 km/hr. The speed in still water is the average, (6 + 14)/2 = 10 km/hr.

Multiple choice

A boat goes $24$ km upstream and $28$ km downstream in $6$ hours. It goes $30$ km upstream and $21$ km downstream in $6$ hours and $30$ minutes. The speed of the boat on still water is
  1. $8$ km/hr
  2. $9$ km/hr
  3. $12$ km/hr
  4. $10$ km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 24/u + 28/v = 6; 30/u + 21/v = 6.5. Let x=1/u, y=1/v. 24x + 28y = 6; 30x + 21y = 6.5. Multiply first by 3, second by 4: 72x + 84y = 18; 120x + 84y = 26. Subtract: 48x = 8 => x = 1/6. So u = 6. 24(1/6) + 28y = 6 => 4 + 28y = 6 => 28y = 2 => y = 1/14. So v = 14. Still water speed = (u+v)/2 = (6+14)/2 = 10 km/hr.

Multiple choice

A boat takes $6$ hours to travel $8\ km$ upstream and $32\ km$ downstream and it takes $7$ hours to travel $20\ km$ upstream and $16\ km$ downstream. Find the speed of the boat in still water and the speed of the stream.
  1. $6,2$
  2. $6,1$
  3. $6,7$
  4. $6,9$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 8/u + 32/v = 6 and 20/u + 16/v = 7. Solving this system gives u = 4 and v = 8. Speed of boat = (v + u)/2 = 6, speed of stream = (v - u)/2 = 2.

Multiple choice

A motor boat can travel $30\ km$ upstream and $28\ km$ downstream in $7$ hours. It can travel $21\ km$ upstream and return in $5$ hours. Find the speed of the boat in still water in $km/h$.
  1. $3$
  2. $15$
  3. $10$
  4. $11$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 30/u + 28/v = 7 and 21/u + 21/v = 5. From the second, 1/u + 1/v = 5/21. Let x = 1/u, y = 1/v. 30x + 28y = 7 and 21x + 21y = 5 (or x + y = 5/21). Substituting y = 5/21 - x: 30x + 28(5/21 - x) = 7 => 2x + 20/3 = 7 => 2x = 1/3 => x = 1/6. So u = 6. Then y = 5/21 - 1/6 = (10-7)/42 = 3/42 = 1/14. So v = 14. Speed of boat = (u + v) / 2 = (6 + 14) / 2 = 10 km/h.