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

Raj can row a boat in still water at a speed of m km/hr. It takes him twice the time to row k km upstream than downstream. One day, Raj rows 16 km upstream and 32 km downstream and takes 8 hours, what is the speed of the stream?

  1. 1 km/hr

  2. 2 km/hr

  3. 3 km/hr

  4. 4 km/hr

  5. Can't find
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed be m and stream speed be s. Upstream speed = m-s, downstream = m+s. Time taken: k/(m-s) = 2 * k/(m+s) -> m+s = 2m-2s -> m = 3s. Given 16/(m-s) + 32/(m+s) = 8. Substitute m=3s: 16/(2s) + 32/(4s) = 8 -> 8/s + 8/s = 8 -> 16/s = 8 -> s = 2.

Multiple choice

A boat travels at a speed of 21 miles/hour in still water. The ratio of the speed of the boat upstream to the speed downstream is 2 : 5. Determine the additional time it takes for the boat to travel 72 miles upstream compared to the time it takes to travel the same distance downstream.

  1. 2 hours and 24 minutes

  2. 3 hours and 36 minutes

  3. 4 hours and 46 minutes

  4. 5 hours and 12 minutes

  5. 5 hours and 15 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed be B=21 and current speed be C. Upstream speed (B-C) / Downstream speed (B+C) = 2/5. Solving 5(21-C) = 2(21+C) gives 105-5C = 42+2C, so 7C=63, C=9. Upstream speed = 12, Downstream = 30. Time upstream = 72/12 = 6 hours. Time downstream = 72/30 = 2.4 hours. Difference = 3.6 hours, which is 3 hours 36 minutes.

Multiple choice

Two neighboring towns, Serenityville and Concordburg, are positioned 84 miles apart along the serene Tranquil River. A nimble speedboat travels between these towns, completing the round trip smoothly. The constant current of the river flows at 12 miles per hour. The speedboat manages to finish the entire round trip in over 24 hours, without any breaks in the journey. What is the highest speed of the boat that could achieve in waters (in miles/hour)?

  1. 12

  2. 14

  3. 16

  4. 18

  5. a
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

The ratio of time taken by a boat to cover a certain distance upstream to time taken by the boat to cover same distance downstream is 5 : 3. If the speed of stream is doubled, then the time taken by boat to cover a certain distance downstream will be what percent less than time taken by the boat to cover same distance in still water?

  1. 15

  2. 25.88

  3. 25

  4. 33.33

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

Let boat speed be b and stream speed be s. Upstream time/Downstream time = (b+s)/(b-s) = 5/3, so 3b+3s = 5b-5s, meaning 2b = 8s or b = 4s. If stream speed doubles to 2s, downstream time is d/(b+2s) = d/(4s+2s) = d/6s. Time in still water is d/b = d/4s. The percentage reduction is ((d/4s - d/6s) / (d/4s)) * 100 = (1/4 - 1/6) / (1/4) * 100 = (2/24) / (1/4) * 100 = 33.33%.

Multiple choice

A boat travels downstream from pier X to pier Y at a speed of 15 miles per hour. On the return journey upstream, due to the water current, the boat can travel only at 10 miles per hour. If the one-way distance between the piers is 60 miles, what is the total time taken for a round trip?

  1. 5 hours

  2. 6 hours

  3. 8 hours

  4. 10 hours

  5. 12 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Downstream time = 60 / 15 = 4 hours. Upstream time = 60 / 10 = 6 hours. Total time = 4 + 6 = 10 hours.

Multiple choice

Boat X covers a certain distance downstream in (b - 4) hours, and the same distance upstream in (b + 4) hours. The speed of the boat X in still water is 15 km/hr. The speed of boat Y in still water is equal to the speed of the stream, which is 6 km/hr. Find the distance (in km) covered by boat Y downstream in (b + 2) hours. Assume both boats are operating in the same stream conditions.

  1. 184

  2. 172

  3. 144

  4. 132

  5. 116
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D and stream speed be s=6. Boat X: (15+6)(b-4) = (15-6)(b+4). 21b - 84 = 9b + 36, so 12b = 120, b = 10. Distance D = 21 * (10-4) = 126 km. Boat Y speed in still water is 6 km/hr. Downstream speed of Y = 6+6 = 12 km/hr. Distance covered in (10+2) hours = 12 * 12 = 144 km.

Multiple choice

The speed of a boat while moving a particular distance downstream is 25 m/s. Its speed in still water is 18 m/s. What is the ratio of time taken by the same boat to cover an equal distance in upstream and then, in downstream direction?

  1. 25 : 11

  2. 11 : 25

  3. 64 : 22

  4. 22 : 64

  5. 64 : 11
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Downstream speed = 25 m/s. Still water speed = 18 m/s. Stream speed = 25 - 18 = 7 m/s. Upstream speed = 18 - 7 = 11 m/s. Time taken for distance D: Upstream time = D/11, Downstream time = D/25. Ratio of Upstream time to Downstream time = (D/11) / (D/25) = 25/11.

Multiple choice

A boat owner sets off on a river journey. The boat travels 150 km upstream in 12 hours and covers the same distance downstream in 10 hours. On the next day, the boat departs from a point M and follows this pattern: it travels downstream for 4 hours, then upstream for 4 hours. This cycle is repeated for a total of 3 times. After completing these 3 cycles, the boat will be:

  1. 24 km downstream of point M

  2. 30 km downstream of point M

  3. 36 km downstream of point M

  4. 48 km downstream of point M
Reveal answer Fill a bubble to check yourself
B Correct answer