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

A boat moves along the flow of of river between two fixed points P and Q. It takes 40 minutes when going downstream and takes 120 minutes when going upstream between these two points. What time it will take in still water to cover the distance equal to PQ?

  1. 50 minute

  2. 100 minute

  3. 60 minute

  4. 90 minute
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v be boat speed and u be stream speed. Downstream: v + u = D/40. Upstream: v - u = D/120. Adding these: 2v = D/40 + D/120 = 3D/120 + D/120 = 4D/120 = D/30. Thus, v = D/60. The time taken in still water is D/v = 60 minutes.

Multiple choice

A boat which can moves with a speed of $5$$\mathrm { m } /$ s relative to water crosses a river of width $480$$\mathrm { m }$ flowing with a constant speed of $4$$\mathrm { m } / \mathrm { s } .$ What is the time taken by the boat to cross the tiver along the shortest path.
  1. $80$ $\mathrm { s }$
  2. $160$$\mathrm { s }$
  3. $240$$\mathrm { s }$
  4. $320$$\mathrm { s }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Shortest path means crossing perpendicular to the flow. Speed relative to ground = sqrt(5^2 - 4^2) = 3 m/s. Time = Width / Speed = 480 / 3 = 160 s.

Multiple choice

A motot boat covers the distance between two spots on the river banks in $t_1=8h$ and $t_2=12h$ in down stream and upstream respectively. The time required for the boat to cover this distance in still water will be:
  1. $6.9$ hr
  2. $9.6$ hr
  3. $69$ second
  4. $96$ second
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the still-water speed be u and the stream speed be v. The downstream and upstream speeds are D/8 and D/12, so 2u = D/8 + D/12 = 5D/24. Therefore, the still-water travel time is D/u = 48/5 = 9.6 hours.

Multiple choice

Statement 1 : The magnitude of velocity of two boats relative to river is same. Both starts simultaneously from same point on one bank and they may reach opposite bank simultaneously moving along different paths. Statement 2 : For boats to cross the river in same time.The component of their velocity relative to river in direction normal to flow should be same.

  1. Statement -1 is false , Statement- 2 is true.

  2. Statement-1 is true, Statement-2 is true , Statement-2 is a correct explanation for statement-1

  3. Statement-1 is true , Statement-2 is true; Statement-2 is not a correct explanation for statement-1

  4. Statement -1 is true, Statement-2 is false.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement 1 is true because boats can reach the opposite bank simultaneously by adjusting their paths to compensate for the river flow. Statement 2 is true because the time to cross is determined only by the velocity component perpendicular to the flow; if this component is the same for both, they cross in the same time regardless of the path.

Multiple choice

A motor boat covers the distance between two places on a river and returns in $14 \ hrs$. If the velocity of the boat in still water is $35 \ km/h$ and velocity of water in the river is $5 \ km/h$, then the distance between the two places is
  1. $100 \ km$
  2. $240 \ km$
  3. $220\  km$
  4. $180\  km$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let d be the distance. Speed downstream = 35 + 5 = 40 km/h. Speed upstream = 35 - 5 = 30 km/h. Time = d/40 + d/30 = 14. (3d + 4d) / 120 = 14. 7d / 120 = 14. d = 240 km.

Multiple choice

Set the drifts suffered by boat in decreasing order. a) $d = 1000 m$ ; V${r}$= 2 ms$^{-1}$ ; V${b}$= 4 ms$^{-1}$ b) $d = 500 m$ ; V${r}$= 1 ms$^{-1}$ ; V${b}$= 6 ms$^{-1}$ c) $d = 1000 m$ ; V${r}$= 6 ms$^{-1}$ ; V${b}$= 6 ms$^{-1}$ [Here $d =$ width of river, V${r}$= Velocity of water in river ; V${b}$= Velocity of boat in still water]
  1. $a, b, c$
  2. $b, c, a$
  3. $c, a, b$
  4. $c, b, a$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Drift = (Vr / Vb) * d. a) (2/4) * 1000 = 500. b) (1/6) * 500 = 83.3. c) (6/6) * 1000 = 1000. Decreasing order: c (1000), a (500), b (83.3).

Multiple choice

The width of river is 1 km. The velocity of boatis 5 km/hr. The boat covered the width of riverwith shortest will possible path in 15 min. Thenthe velocity of river stream is :

  1. 3 km/hr

  2. 4 km/hr
  3. $\sqrt { 29 } km/hr$
  4. $\sqrt { 41 } km/hr$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The boat crosses the 1 km width in 15 minutes (0.25 hours). The resultant velocity is 1/0.25 = 4 km/hr. Since the boat moves with the shortest path, the velocity of the boat (5 km/hr) is the hypotenuse, and the river velocity (v) and resultant velocity (4 km/hr) are legs. 5^2 = 4^2 + v^2, so v = 3 km/hr.

Multiple choice

A $600$ meter wide river flows directly south at $4.0m/s$. A small motor boat travels at $5.0m/s$ in still water and points in such a direction so that it will travel directly east relative to the land. The time taken it takes to cross the river is closest to
  1. $67s$
  2. $120s$
  3. $150s$
  4. $200s$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The river flows south at 4 m/s. The boat travels at 5 m/s in still water. To travel directly east, the boat must point upstream (north) to cancel the river's flow. The velocity component perpendicular to the river is sqrt(5^2 - 4^2) = 3 m/s. Time = Distance / Velocity = 600 m / 3 m/s = 200 s.

Multiple choice

A boat moving perpendicular to the bank with a velocity of $7.2$ km/h. The current carries it $150$m downstream, find the velocity of the current.(The width of the river is $0.5$ km).
  1. $0.4 ms^{-1}$
  2. $1.2 ms^{-1}$
  3. $0.5 ms^{-1}$
  4. $0.6 ms^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Time to cross river = Width / Velocity_boat = 0.5 km / 7.2 km/h = 1/14.4 hours = 1/14.4 * 3600 seconds = 250 seconds. Drift = Velocity_current * Time. 0.15 km = V_c * (1/14.4) -> V_c = 0.15 * 14.4 = 2.16 km/h. 2.16 * 1000 / 3600 = 0.6 m/s.