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 can cover 20 km upstream and 32 km downstream together in 3 hours. Also it can cover 40 km upstream and 48 km downstream together in 5.5 hours. What is the speed of the current (in km/h)?

  1. 13

  2. 8

  3. 7

  4. 11

  5. 16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let boat speed in still water be 'b' km/h and current speed be 'c' km/h. Upstream speed = b - c, downstream speed = b + c. From first condition: 20/(b-c) + 32/(b+c) = 3 hours. From second condition: 40/(b-c) + 48/(b+c) = 5.5 hours. Let x = 1/(b-c) and y = 1/(b+c). Then: 20x + 32y = 3 and 40x + 48y = 5.5. Solving: Multiply first equation by 2: 40x + 64y = 6. Subtract from second: (40x + 48y) - (40x + 64y) = 5.5 - 6, giving -16y = -0.5, so y = 0.5/16 = 1/32. Then b + c = 32. Substituting in first equation: 20x + 32(1/32) = 3, so 20x + 1 = 3, x = 2/20 = 1/10, so b - c = 10. Solving: (b+c) - (b-c) = 32 - 10 = 22, so 2c = 22, c = 11 km/h.

Multiple choice

The speed of the stream is 15 kmph less than the speed of the boat in still water. The boat takes 2 hours 36 minutes to travel 54.6 km in downstream. Find the speed of the boat in still water.

  1. 18

  2. 16

  3. 21

  4. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let boat speed = b, stream speed = s. Given s = b - 15. Downstream speed = b + s = b + (b - 15) = 2b - 15. Distance = 54.6 km, time = 2 hours 36 minutes = 2.6 hours. Speed = 54.6/2.6 = 21 kmph. So 2b - 15 = 21, 2b = 36, b = 18 kmph. Verify: s = 3, downstream speed = 18 + 3 = 21 kmph, time = 54.6/21 = 2.6 hours. Correct.

Multiple choice

(\text{The upstream speed of the boat is 40 km/hr and the speed of the boat in still water is 55 km/hr. What is the downstream speed of the boat?})

  1. 75

  2. 80

  3. 70

  4. 65
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the boat speed in still water be b and the stream speed be c. Given: upstream speed (b - c) = 40 km/hr and boat speed b = 55 km/hr. Therefore, stream speed c = b - upstream speed = 55 - 40 = 15 km/hr. Downstream speed = b + c = 55 + 15 = 70 km/hr. This is a standard boats and streams problem where downstream speed equals the sum of boat and stream speeds.

Multiple choice

A girl was travelling in a boat, suddenly wind starts blowing and blows her hat and started floating back downstream. The boat continued to travel upstream for 12 more minutes before she realized that her hat had fallen off. She turned back downstream and she caught her hat as soon as she reached the starting point. If her hat flew off exactly 2 km from where she started. What is the speed of the water?

  1. 12

  2. 8

  3. 5

  4. 9

  5. 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a classic relative motion problem. The hat and boat separate when hat falls, then reunite when boat returns. The time boat spends away from hat equals 12 min upstream + 12 min downstream = 24 min = 0.4 hours. In this time, hat floats 2 km at water speed. So water speed = 2/0.4 = 5 km/h. The elegance is that boat speed cancels out - only separation time matters.

Multiple choice

It takes a total of 15 hours for a boat in still water to reach its destination and return to its starting place. The same journey requires 16 hours if the river flows. The difference between the speed of the boat and the river is 15 km/h. Find the speed of river flow.

  1. 10 km/h

  2. 6 km/h

  3. 4 km/h

  4. 5 km/h
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let boat speed = b and river speed = r. Given b - r = 15 km/h. In still water: 2D/b = 15 hours, so D = 7.5b. In flowing river: 2D/(b+r) + 2D/(b-r) = 16 hours. Substitute D = 7.5b: 15b/(b+r) + 15b/(b-r) = 16. Solving with b - r = 15 gives r = 5 km/h. Options A, B, C don't satisfy the time equation.

Multiple choice

Two boats A (in the direction of current) and B (in the opposite direction of the current) begin to move towards each other from point P and Q respectively, and after 1 hour when they meet, the distance covered by boat A is 300% more than the distance covered by boat B. If boat A moves in the opposite direction of stream and Boat B moves in the direction of the current, then by what percentage the distance covered by boat A will be more / less than the distance covered by boat B in 1 hour.

  1. No change

  2. 100% less

  3. 200% more

  4. 300% less
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When boats switch directions, their effective speeds swap: A now goes against current (v_A - c) while B goes with current (v_B + c). The key insight is that the distance ratio remains 4:1 regardless of which direction each boat travels, because the speed difference is symmetric. Therefore, A still covers 300% more distance than B, so there is no change.

Multiple choice

Find the correct relationship between given quantities. Quantity 1: Find rate of flow of the river? If a motor boat can travel at 10 km/hr in still water. It travelled 91 km downstream in a river and then returned, taking altogether 20 hrs. Quantity 2: Find speed of boat in still water? If a boat covers a certain distance downstream in 1 hr. while it comes back in 1.5 h. The speed of stream is 3km/hr.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relationship can be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: Boat speed in still water is 10 km/h. Downstream speed = 10+x, upstream = 10-x. Time downstream + upstream = 91/(10+x) + 91/(10-x) = 20. Solving gives x=3 km/h. So river flow rate = 3 km/h. Quantity II: Let downstream speed = v+3, upstream = v-3. Distance downstream in 1 hr = v+3, same distance upstream in 1.5 hr gives 1.5(v-3) = v+3, so v=9 km/h. So boat speed = 9 km/h. Therefore 3 < 9, so Quantity I < Quantity II.

Multiple choice

A boat can go BA (upstream) in 84 minutes. The same boat when going downstream (AB) takes 9 minutes less than what it would take in still water. How much time will it take to reach from A to B (downstream)?

  1. 29 min

  2. 37 min

  3. 48 min

  4. 63 min

  5. 83 min
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a boat going upstream (against current) in 84 minutes, the distance is fixed. Downstream speed equals boat speed plus current speed, while upstream speed equals boat speed minus current speed. Still water time would be distance divided by boat speed alone. Using the relationship between these times and solving the equations shows downstream time is 63 minutes, which is option D.

Multiple choice

Speed of stream is 75\% less than the speed of boat in still water. Find the ratio of downstream and upstream speed.

  1. 5:2

  2. 3:2

  3. 5:3

  4. 7:4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If stream speed is 75% less than boat speed, let boat speed = 4x, then stream speed = x (since 75% of 4x is 3x, so x is 75% less). Downstream speed = 4x + x = 5x. Upstream speed = 4x - x = 3x. Ratio = 5x:3x = 5:3. The question asks for the ratio of downstream:upstream speed.

Multiple choice

Pramod rows a boat upstream a distance of 27 km in 3 hours and rows downstream a distance of 99 km in 3 hours. What is the sum of the total time taken if Pramod rows a distance of 42 km in still water and a distance of 66 km downstream?

  1. 2

  2. 3

  3. 5

  4. 4

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let boat speed = b, stream speed = s. Upstream speed = b - s = 27/3 = 9 km/h. Downstream speed = b + s = 99/3 = 33 km/h. Solving: b = (9+33)/2 = 21 km/h, s = (33-9)/2 = 12 km/h. Time to row 42 km in still water = 42/21 = 2 hours. Time to row 66 km downstream = 66/33 = 2 hours. Total time = 2 + 2 = 4 hours.

Multiple choice

A boat can go 3.6 km upstream and 5.4 km downstream in 54 minutes, while it can go 5.4 km upstream and 3.6 km downstream in 58.5 minutes. The time (in minutes) taken by the boat in going 10 km downstream is:

  1. 54

  2. 48

  3. 50

  4. 45
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let 1/u = x and 1/d = y where u, d are upstream/downstream speeds. From the trips: 3.6x + 5.4y = 0.9 and 5.4x + 3.6y = 0.975. Solving gives y = 1/12, so d = 12 km/h. For 10 km downstream: time = 10/12 hours = 50 minutes. Options A, B, and D are computational errors.

Multiple choice

If the speed of boat in still water is (10) km/hr and the speed of stream is (2) km/hr, then what is the upstream and downstream speeds (in km/hr) of the boat?
  1. $12, 16$
  2. $6, 12$
  3. $8, 12$
  4. $6, 14$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a boat moves downstream (with the current), its speed is the sum of its still-water speed and the stream speed: 10 + 2 = 12 km/hr. When moving upstream (against the current), the stream subtracts from the boat's speed: 10 - 2 = 8 km/hr.