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 man rows to a place 40 km distant and back in a total of 18 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. What is the speed of boat in still water? एक व्यक्ति 40 किमी की दूरी 18 घंटे में खे कर जाता है और वापस आ जाता है। वह पाता है कि जितने समय में वह धारा के अनुकूल 5 किमी खेता है उतने समय में धारा के प्रतिकूल 4 किमी खेता है। शांत जल में नाव की गति क्या है?

  1. 4

  2. 3

  3. 3.5

  4. 4.5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let boat speed in still water be b km/h and stream speed be s km/h. Downstream speed = (b + s) and upstream speed = (b - s). Given: 5/(b + s) = 4/(b - s), so 5(b - s) = 4(b + s), giving b = 9s. Total journey: 40/(b + s) + 40/(b - s) = 18 hours. Substituting b = 9s: 40/(10s) + 40/(8s) = 18, so 4/s + 5/s = 18, giving 9/s = 18, thus s = 0.5 km/h. Therefore b = 9 × 0.5 = 4.5 km/h.

Multiple choice

In one hour a boat goes13 km along the stream and 7 km aganist the stream.The speed of the boat in still water (in km/hr)is- एक घंटे में धारा के साथ एक नाव 13 किमी और धारा के विपरीत 7 किमी जाती है |नाव की गति शांत जल (किमी / घंटा) में है-

  1. 3

  2. 8

  3. 10

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed (with stream) = 13 km/hr, upstream (against) = 7 km/hr. Still water speed = (downstream + upstream)/2 = (13+7)/2 = 10 km/hr. Stream speed = (downstream - upstream)/2 = 3 km/hr. Answer C is correct.

Multiple choice

A boat can travel (\frac{3}{4}) km in downstream in (\frac{4}{5}) hour and return in upstream in (\frac{6}{5}) hour find the ratio of the speed of the boat in still water and speed of current ?

  1. 3 : 2

  2. 5 : 1

  3. 4 : 5

  4. 5 : 4

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

Downstream speed = (3/4)÷(4/5) = 15/16 km/h. Upstream speed = (3/4)÷(6/5) = 5/8 km/h. Let boat speed = b, current speed = c. Then b+c = 15/16 and b-c = 5/8 = 10/16. Adding: 2b = 25/16, so b = 25/32. Then c = 15/16 - 25/32 = 5/32. Ratio b:c = 25/32 : 5/32 = 25:5 = 5:1.

Multiple choice

The speed of a motor -boat is that of the current of water as 36 : 5. The boat goes along with the current in 5 hours 10 minutes. It wil come back in ? मोटर-नाव और धारा की चाल का अनुपात 36 : 5 है . नाव धारा की दिशा में जाने में 5 घंटे और 10 मिनट लेती है तो वापस आने में वह कितन समय लेगी ?

  1. 40/3 hours / घंटे

  2. 41/6 hours / घंटे

  3. 41/7 hours / घंटे

  4. 37/6 hours / घंटे
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Boat speed:current speed = 36:5. Let boat = 36k, current = 5k. Downstream: 41k × 31/6 = distance. Upstream: 31k × time = same distance. Time = (41k × 31/6) / 31k = 41/6 hours.

Multiple choice

A boat has to travel upstream 20 km from point x of a river to point Y. The total time taken by boat in travelling from point X to Y and Y to X is 41 min 40 sec. What is the speed of boat? एक नाव को धारा के ऊर्ध्वप्रवाह नदी के बिन्दु X से बिन्दु Y तक 20 किमी. जाना है। बिन्दु X से Y तक नाव को यात्रा करने में तथा Y से X तक यात्रा करने में लिया गया कुल समय 41 मिनट 40 सेकेण्ड है। नाव की चाल क्या है?

  1. 20 km/hr./ किमी./घण्टा

  2. 24 km/hr./ किमी./घण्टा

  3. 48 km/hr./ किमी./घण्टा

  4. Can't be determined/निर्धारित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know the one-way distance is 20 km and total time for round trip is 41 min 40 sec = 2500 seconds. Let boat speed = b, stream speed = s. Upstream: 20/(b-s) + Downstream: 20/(b+s) = 2500/3600 hours. This is one equation with two unknowns (b and s). We cannot determine boat speed uniquely without knowing the stream speed. Options A, B, and C are specific values that can't be verified.

Multiple choice

The speed of a boat in still water 11 km/hr. It can go 12 km upstream and return downstream to the engine point in 2hr 45min. What is the speed of stream? स्थिर जल में एक नाव की चाल 11किमी./घंटा है। वह 2 घंटे 45 मिनट में धारा के प्रतिकूल 12 किमी. जाकर अनुप्रवाह में इंजन बिन्दु तक वापस आ सकती है तो धारा की चाल क्या है?

  1. 5 km/hr./किमी./घंटा

  2. 4 km/hr../किमी./घंटा

  3. 3 km/hr../किमी./घंटा

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

Let stream speed = x km/hr. Upstream speed = (11-x), downstream = (11+x). Time upstream: 12/(11-x), time downstream: 12/(11+x). Total time = 2hr 45min = 11/4 hr. Solving 12/(11-x) + 12/(11+x) = 11/4 gives x = 5 km/hr. Verify: 12/6 + 12/16 = 2 + 0.75 = 2.75 hr ✓

Multiple choice

A motor boat can travel at 8 km/hour in still water. It travelled 60 km downstream in a river and then returned to the same place in 20 hours. Find the rate of flow of river. एक मोटर-बोट शांत जल में 8 किमी/घं. की गति से चल सकती है। वह नदी में 60 किमी. अनुप्रवाह चली और वही लौट आयी। उसे कुल 20 घंटे लगे। नदी के प्रवाह की गति क्या है?

  1. 2 km/h/किमी/घं.

  2. 3 km/h/किमी/घं.

  3. 4 km/h/किमी/घं.

  4. 3.5 km/h/किमी/घं.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the river flow at v km/h. Downstream speed = 8+v km/h, upstream speed = 8-v km/h. Time downstream = 60/(8+v), time upstream = 60/(8-v). Total time: 60/(8+v) + 60/(8-v) = 20. Multiplying by (8+v)(8-v): 60(8-v) + 60(8+v) = 20(64-v²). This simplifies to 960 = 1280 - 20v², so 20v² = 320 and v² = 16. Therefore v = 4 km/h.

Multiple choice

A boat goes downstream at the rate of 18 kmph and upstream at the rate of 12 kmph. Find the speed of the boat.

  1. 10 kmph

  2. 12 kmph

  3. 15 kmph

  4. 18 kmph

  5. 8 kmph
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = boat speed + stream speed = 18 kmph. Upstream speed = boat speed - stream speed = 12 kmph. Adding these two equations: 2 × boat speed = 30, so boat speed = 15 kmph. The stream speed is 3 kmph (18 - 15 = 15 - 12 = 3). Option C (15 kmph) is correct.

Multiple choice

If a boat goes 100 km downstream in 10 hours and 75 km upstream in 15 hours, then the speed of stream is- यदि एक नाव 10 घंटें में धारा की दिशा में 100 किमी. चलती है और धारा के विरूद्ध 15 घण्टों में 75 किमी. चलती है, तो धारा की चाल कितनी है?

  1. 2 km/hr./किमी/घं.

  2. 3 km/hr./किमी/घं.

  3. 2.5 km/hr./किमी/घं.

  4. 3.5 km/hr./किमी/घं.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = 100/10 = 10 km/hr, Upstream speed = 75/15 = 5 km/hr. Let boat speed = b, stream speed = s. Then b + s = 10 and b - s = 5. Adding: 2b = 15, so b = 7.5 km/hr. Subtracting: 2s = 5, so s = 2.5 km/hr.

Multiple choice

A boat can cover upstream 24 km. in 6 hours and returns downstream 20 km. in 4 hours. Then find the speed of boat in still water? एक नाव धारा की विपरीत दिशा में 24 किमी. 6 घण्टा में और धारा की दिशा में 20 किमी. 4 घण्टा में चलता है तो नाव की चाल स्थिर जल में बताइये?

  1. 4.5 km./hr./किमी./घं.

  2. 4 km./hr./किमी./घं.

  3. 3.5 km./hr./किमी./घं.

  4. 3 km./hr./किमी./घं.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Upstream speed = 24/6 = 4 km/hr. Downstream speed = 20/4 = 5 km/hr. Speed of boat in still water = (upstream + downstream)/2 = (4+5)/2 = 4.5 km/hr. Option A is correct.

Multiple choice

The speed of current is 5 km./hr. A motorboat goes 10 km. upstream and back again to the starting point in 50 minutes. The speed in km./hr. of the motor boat in still water is - एक धारा की चाल 5 किमी./घं. है। एक मोटरवोट धारा के विपरीत 10 किमी. जाने में और वापस आरम्भिक बिन्दु पर आने में 50 मिनट लेती है। तो स्थिर पानी में उस मोटर बोट की गति कितने किमी./घं. होगी?

  1. 20

  2. 26

  3. 25

  4. 28
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed in still water = x km/hr. Speed upstream = x - 5, speed downstream = x + 5. Time upstream + time downstream = 50/60 hr. So 10/(x-5) + 10/(x+5) = 50/60 = 5/6. Multiplying through: 60(x+5) + 60(x-5) = 5(x²-25). This gives 5x² - 120x - 175 = 0, or x² - 24x - 35 = 0. Factoring: (x - 25)(x + 1) = 0, so x = 25 km/hr.

Multiple choice

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes.How long will it take to go 5 km in stationary water? एक नाविक धारा के विपरीत 2 किमी 1 घण्टे में जाता है और धारा के ओर 1 किमी 10 मिनट में जाता है, तो शान्त जल में 5 किमी. जाने में कितना समय लगेगा?

  1. 40 minute/मिनट

  2. 1 hours 15 min/1घंटे 15 मिनट

  3. 1 hours/ 1घंटे

  4. 1 hours 30 min/1 घंटे 30 मिनट
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Against current: speed = 2 km in 1 hr = 2 km/hr. This is boat speed - current speed. Along current: speed = 1 km in 10 min = 6 km/hr. This is boat speed + current speed. Adding both equations: 2(boat speed) = 8 km/hr, so boat speed = 4 km/hr in still water. Time for 5 km = 5/4 hr = 1.25 hours = 1 hr 15 min.

Multiple choice

A boat covers 48 km. upstream and 72 km. downstream in 12 hours, while it covers 72 km. upstream and 48 km. downstream in 13 hours. The speed of stream is - एक बोट 12 घंटे में 48 किमी. धारा के विरूद्ध तथा 72 किमी. धारा के सापेक्ष जाती है जबकि 13 घंटे में 72 किमी. धारा के विरूद्ध तथा 48 किमी. धारा के सापेक्ष जाती है। धारा की चाल क्या है?

  1. 2 km./hr./किमी./घं.

  2. 2.2 km./hr./किमी./घं.

  3. 2.5 km./hr./किमी./घं.

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

Let boat speed = b, stream speed = s. Upstream speed = b-s, downstream = b+s. 48/(b-s) + 72/(b+s) = 12 and 72/(b-s) + 48/(b+s) = 13. Adding: 120/(b-s) + 120/(b+s) = 25. Also subtracting gives 24/(b-s) - 24/(b+s) = 1. Solving gives s = 2 km/hr.

Multiple choice

The speed of the boat in still water is 16 km/hr and speed of the current is 2 km/hr. It takes a total of 6.5 hours to row upstream from point A to point B and downstream from point B to point C. If the distance from point A to point B is two third the distance between point B and C, what is the total distance travelled by the boat?(in km)

  1. 52.5

  2. 77

  3. 87.5

  4. 105

  5. 154
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The boat's upstream speed is 16-2=14 km/hr and downstream speed is 16+2=18 km/hr. Let BC = d km, so AB = (2/3)d km. Total time = (2d/3)/14 + d/18 = 6.5 hours. Solving gives d = 63 km, so AB = 42 km. Total distance = 63 + 42 = 105 km. Option D (105 km) is correct.

Multiple choice

A boat running downstream takes 4 hrs to go to a place. In what time will it come to the same place if the ratio of speed of boat in still water and that of stream is 5:3?

  1. 15 hrs

  2. 10 hrs

  3. 08 hrs

  4. 12 hrs

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

Boat speed:stream speed=5:3, so let B=5k, S=3k. Downstream speed=B+S=8k takes 4 hours. Upstream speed=B-S=2k will take (8k/2k)×4=16 hours (same distance, inverse ratio of speeds). This elegantly uses the concept that time is inversely proportional to speed for constant distance. The answer 16 hours matches option E.