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 goes upstream 21 miles and downstream 42 miles in 13 hours. Under identical circumstances, it also goes upstream 36 miles and downstream 49 miles in 19 hours. Find the speed of the flow of water in the stream and that of the boat in a fresh-water lake where the water is still, respectively. Both the speeds are to be determined in miles per hour.

  1. 3, 6

  2. 3, 5

  3. 2, 5

  4. 2, 4

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

Let boat speed be x, stream speed be y. Upstream speed = x-y, downstream = x+y. 21/(x-y) + 42/(x+y) = 13 and 36/(x-y) + 49/(x+y) = 19. Solving this system gives x=5, y=2.

Multiple choice

The speed of a stream is 3 km/hr. A boat goes 36 km and comes back to the starting point in 9 hours. What is the speed (in km/hr) of the boat in still water?

  1. 8

  2. 9

  3. 10

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

Let v be the speed in still water. Upstream speed = v-3, downstream = v+3. Time = 36/(v-3) + 36/(v+3) = 9. Divide by 9: 4/(v-3) + 4/(v+3) = 1. 4(v+3) + 4(v-3) = (v-3)(v+3). 4v + 12 + 4v - 12 = v^2 - 9. 8v = v^2 - 9. v^2 - 8v - 9 = 0. (v-9)(v+1) = 0. v = 9.

Multiple choice

The ratio of speed of a motor boat to that of the current of water is 36 : 5. The boat goes along with the current in 5 hours 10 minutes. It will come back in

  1. 5 hr 50 min

  2. 6 hr

  3. 6 hr 50 min

  4. 12 hr 10 min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio of boat speed (b) to current (c) = 36:5. Downstream speed = 41 units, upstream = 31 units. Time downstream = 5 hr 10 min = 310 min. Distance = 41 * 310. Time upstream = (41 * 310) / 31 = 410 min = 6 hr 50 min.

Multiple choice

A boat can cover 30 km going upstream in 20 minutes and 40 km going downstream in 24 minutes. How much time will the boat take to travel 84 km downstream if the speed of the stream is doubled?

  1. 48 minutes

  2. 46 minutes

  3. 36 minutes

  4. 24 minutes

  5. NA
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Upstream speed = 30 / (20/60) = 90 km/h. Downstream speed = 40 / (24/60) = 100 km/h. Let boat speed be u and stream speed be v. u - v = 90, u + v = 100. 2u = 190, u = 95, v = 5. New stream speed = 2 * 5 = 10. New downstream speed = u + 2v = 95 + 10 = 105 km/h. Time for 84 km = 84 / 105 hours = 0.8 hours = 48 minutes.

Multiple choice

A boat travels upstream from A to B and comes back downstream from B to A in 5 hours and 20 minutes. B is the midpoint of the distance AC. Find the time taken by the boat to travel back from C to A, if it takes 6 hours to travel from A to C going upstream.

  1. 4 hours

  2. 1 hour and 20 minutes

  3. 3 hours and 40 minutes

  4. 4 hours and 40 minutes

  5. 3 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let v be boat speed and u be stream speed. Upstream time A to C is 6 hours, so AC = 6(v-u). Since B is the midpoint, AB = BC = 3(v-u). Upstream A to B is 3 hours, so downstream B to A is 5h 20m - 3h = 2h 20m. Downstream speed is BC/time = 3(v-u) / (7/3) = 9(v-u)/7. Downstream time C to A is AC / (downstream speed) = 6(v-u) / (9(v-u)/7) = 42/9 = 4 hours 40 minutes.

Multiple choice

Find the speed of flow of water in a stream if a motorboat takes exactly 90 minutes less to travel a distance of 36 miles downstream than to travel the exact same distance upstream. [Note: Speed of the boat in still water is 10 mph]

  1. 2 mph

  2. 3 mph

  3. 4 mph

  4. 5 mph

  5. 6 mph
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let v be the stream speed. Downstream speed is 10+v, upstream is 10-v. Time difference: 36/(10-v) - 36/(10+v) = 1.5 hours. Solving 36(10+v) - 36(10-v) = 1.5(100-v^2) leads to 72v = 150 - 1.5v^2, or v^2 + 48v - 100 = 0. Factoring gives (v+50)(v-2) = 0, so v = 2.

Multiple choice

Directions: In the following question, we have two quantities given. Compare these quantities and answer accordingly with the following given options. Quantity I: A boat goes 17 km along the stream in 1 hour and 9 km against the stream in 1 hour. The speed of the boat in still water. Quantity II: 10 km/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 relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let boat speed be B and stream speed be S. B+S = 17, B-S = 9. Adding equations: 2B = 26, B = 13 km/hr. Quantity I (13) > Quantity II (10).

Multiple choice

Directions: Study the given information carefully to answer the question that follows: The speeds of Boat A and Boat B are in the ratio 4 : 5. The speed of the current with respect to Boat A is 1/4th and with respect to Boat B is 1/5th. If the distances covered by Boat A and Boat B are the same while going upstream and downstream respectively, then the ratio of times taken by Boat A and Boat B is

  1. 1 : 2

  2. 1 : 3

  3. 2 : 1

  4. 2 : 3

  5. 2 : 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be 4v and 5v. Current speed for A is v (1/4 of 4v) and for B is v (1/5 of 5v). Downstream speed for B = 5v + v = 6v. Upstream speed for A = 4v - v = 3v. Distance = Speed * Time. Since distances are equal, 3v * Ta = 6v * Tb, so Ta/Tb = 6/3 = 2/1.

Multiple choice

A boat can go 30 km downstream and 24 km upstream in 2 hours 27 minutes. Also, it can go 10 km downstream and 4 km upstream in 37 minutes. What is the speed of the boat upstream (in km/h)?

  1. 24

  2. 18

  3. 22

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let d be the downstream speed and u be the upstream speed. From the given conditions, we set up two equations: 30/d + 24/u = 147/60 and 10/d + 4/u = 37/60. Multiplying the second equation by 3 and subtracting it from the first equation eliminates d, giving 12/u = 36/60, which simplifies to an upstream speed of 20 km/h.

Multiple choice

In a stream running at 2 kmph, a boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of the boat in still water.

  1. 8 km/hr.

  2. 11 km/hr.

  3. 22 km/hr.

  4. 17 km/hr.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed in still water be b kmph. Upstream speed = b-2 kmph, downstream speed = b+2 kmph. Time upstream = 10/(b-2) hours, time downstream = 10/(b+2) hours. Total time = 10/(b-2) + 10/(b+2) = 55/60 hours. Solving gives b = 22 kmph. Option A (8 kmph) is too slow - the boat would barely move upstream. Option B (11 kmph) is a common error from incorrect equation setup. Option D (17 kmph) doesn't satisfy the time equation.

Multiple choice

The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return downstream to the engine point in 2 hours 45 minute. What is the speed of stream?

  1. 5 km/hr

  2. 4 km/hr

  3. 3 km/hr

  4. 2 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let stream speed = s km/hr. Upstream speed = 11-s, downstream speed = 11+s. Time upstream + time downstream = 12/(11-s) + 12/(11+s) = 2.75 hours. Solving: 12(11+s + 11-s)/((11-s)(11+s)) = 2.75, so 264/(121-s²) = 2.75. This gives s² = 25, so s = 5 km/hr. The answer must be positive since speed can't be negative.