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 goes 12 km upstream and back again to the starting point in 4 hours. If the speed of water is 4 km/hr. Find the speed of the boat. एक आदमी 12 किमी.ऊर्ध्वप्रवाह जाता है और प्रारम्भिक बिंदु पर आने में 4 घंटे लेता है | यदि जल की गति 4 किमी./घंटा है | नाव की गति ज्ञात कीजिये |

  1. 6.5 km./किमी.

  2. 7 km./किमी.

  3. 8 km./किमी.

  4. 5 km./किमी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = b. Upstream speed = b - 4, downstream speed = b + 4. Total time: 12/(b-4) + 12/(b+4) = 4. Solving gives b = 8 km/hr. Check: 12/4 + 12/12 = 3 + 1 = 4 hours.

Multiple choice

A boatman can row his boat 2 km in 20 minutes against the stream and returns in 15 minutes. Then what is the speed of the boat in still water?

  1. 1 km/hr.

  2. 8 km/hr.

  3. 7 km/hr.

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

Upstream speed = 2 km / 20 min = 6 km/hr (boat - stream). Downstream speed = 2 km / 15 min = 8 km/hr (boat + stream). Let boat speed = b, stream speed = s. Then b - s = 6 and b + s = 8. Adding: 2b = 14, so b = 7 km/hr. Option C is correct.

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 time 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 A to point B is two - third of the distance between point B and C. What is the distance between points B and C. स्थिर जल में नाव की चाल 16 किमी./घण्टा है और धारा की चाल 2 किमी./घण्टा है। यह बिन्दु A से बिन्दु B तक ऊर्ध्वप्रवाह में और बिन्दु B से बिन्दु C तक अनुप्रवाह जाने में कुल समय 6.5 घण्टे लेती है। यदि बिन्दु A से बिन्दु B तक की दूरी बिन्दु B से बिन्दु C के बीच की दूरी का दो-तिहाई है तो बिन्दु B और बिन्दु C के बीच की दूरी क्या है?

  1. 62 km./ किमी.

  2. 63 km./ किमी.

  3. 64 km./ किमी.

  4. 65 km./ किमी.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed upstream = 16 - 2 = 14 km/h, downstream = 16 + 2 = 18 km/h. Let AB = d, then BC = 3d/2. Total time = d/14 + (3d/2)/18 = 6.5. Simplifying: d/14 + d/12 = 6.5, so (6d + 7d)/84 = 6.5, giving 13d = 546. Therefore d = 42 km and BC = 3 × 42/2 = 63 km.

Multiple choice

The speed of a boat in still water is 9.5 kmph while that of current is 2.5 kmph. If the boat takes 285 minutes in rowing form point A to B and coming back to point A, what is the distance between point A and B ? एक नाव की स्थिर जल में चाल 9.5 किमी/घंटा है जबकि धारा की 2.5 किमी/घंटा है। यदि नाव बिन्दु A से B तक जाकर वापस बिन्दु A तक लौटने में 285 मिनट लेती है तो बिन्दु A और B की बीच की दूरी क्या है ?

  1. 24 km/किमी

  2. 21 km/किमी

  3. 8.5 km/किमी

  4. 15 km/किमी
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Boat speed in still water = 9.5 kmph, current speed = 2.5 kmph. Downstream speed = 12 kmph, upstream speed = 7 kmph. Total time = 285 minutes = 4.75 hours. If distance is d: d/12 + d/7 = 4.75. Solving: 7d + 12d = 4.75 × 84, so 19d = 399, giving d = 21 km. This tests boats and streams concepts.

Multiple choice

A motor boat goes 2 km upstream in a stream flowing at the rate of 3 km per hour and then returns downstream to the starting point in 30 minutes. Find the speed of the motor boat in still water. एक मोटर बोट 2 किमी. ऊर्ध्वप्रवाह में 3 किमी.प्रति घंटे की चाल से गति करती है और फिर अनुप्रवाह में गति करते हुए मूल बिंदु पर 30 मिनट में पहुँचती है। स्थिर जल में मोटर बोट की चाल ज्ञात कीजिये।

  1. 9.5 kmph/किमी./घंटा

  2. 8.5 kmph/किमी./घंटा

  3. 9 kmph/किमी./घंटा

  4. 8 kmph/किमी./घंटा
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed in still water = b kmph. Stream speed = 3 kmph. Upstream speed = b - 3, time = 2/(b-3) hours. Downstream speed = b + 3, time = 2/(b+3) hours. Total time = 30 min = 0.5 hours. So 2/(b-3) + 2/(b+3) = 0.5. Solving: 4b/(b²-9) = 0.5, so 8b = b² - 9, giving b² - 8b - 9 = 0. So b = 9 kmph (ignoring negative solution).

Multiple choice

The ratio between the speed of boat to the current of water is 36 : 5. The boat goes along with the current in 5 hours 10 minutes. It will come back in नाव की चाल और पानी की धारा की चाल में अनुपात 36 : 5 है | नाव धारा की चाल के अनुकूल 5 घंटे 10 मिनट में जाती है | यह वापस आएगी

  1. 6 hours

  2. 5 hours 50 minutes

  3. 6 hours 50 minutes

  4. 12 hours 10 minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = 36x and current speed = 5x. Downstream speed = 36x + 5x = 41x. Upstream speed = 36x - 5x = 31x. Time taken is inversely proportional to speed for the same distance. Downstream time = 5 hours 10 minutes = 31/6 hours. Upstream time = Downstream time × (Downstream speed/Upstream speed) = (31/6) × (41/31) = 41/6 = 6 hours 50 minutes. The ratio method avoids calculating x and distance separately - the key insight is that time ratios are inverse of speed ratios.

Multiple choice

A boat takes double of the time taken by it to go downstream while coming in upstream. If speed of the current is 3 km/hr. Find how much percent more the speed of the boat is ? एक नाव धारा के ऊर्ध्वप्रवाह जाने में अनुप्रवाह जाने में लगे समय का दोगुना लेती है | यदि धारा की चाल 3 किमी./घंटा है | ज्ञात कीजिये कि नाव की चाल, धारा की चाल से कितने प्रतिशत अधिक है ?

  1. 200%

  2. 300%

  3. 100%

  4. 0%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let boat speed = b, current speed = c = 3 km/hr. Downstream speed = b + c, upstream speed = b - c. Time upstream = 2 × Time downstream, so distance/(b-c) = 2 × distance/(b+c). This gives b + c = 2(b - c), so b = 3c = 9 km/hr. Percentage more = (9-3)/3 × 100 = 200%.

Multiple choice

A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is एक नाव एक निश्चित दूरी को अनुप्रवाह तय करने में ऊर्ध्वप्रवाह की तुलना में आधा समय लेती है | स्थिर जल में नाव की चाल का धारा की चाल से अनुपात है

  1. 2 : 1

  2. 1 : 2

  3. 4 : 3

  4. 3 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let boat speed = b, current speed = c. Downstream: b+c, upstream: b-c. Time ratio upstream:downstream = 2:1, so speed ratio (downstream:upstream) = 2:1. Thus (b+c)/(b-c) = 2/1, giving b+c = 2b-2c, so b = 3c, or b:c = 3:1. Verification: If b=3, c=1, downstream=4, upstream=2, time ratio = 1:2 ✓

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. 2 किमी/घं. के प्रवाह में एक नाव प्रवाह के विरूद्ध 10 किमी जाती है और वापस अपने प्रारम्भिक बिंदु पर 55 मिनट में आ जाती है। शांत जल में नाव की चाल ज्ञात कीजिये-

  1. 8 km/hr./किमी/घं.

  2. 11 km/hr./किमी/घं.

  3. 22 km/hr.किमी/घं.

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

Let boat speed in still water be v. Upstream speed is (v-2), downstream is (v+2). Total time: 10/(v-2) + 10/(v+2) = 55/60. Solving gives v = 22 km/hr. The key is setting up the time equation correctly.

Multiple choice

The distance between two points is 36 km. A boat rows in still water at 6kmph, it takes 8hr less to cover distance in downstream in comparison to that in upstream. Find the rate of stream. दो बिन्दुओं के बीच की दूरी 36 किमी. है | एक नाव स्थिर जल में 6 किमी./घंटा की चाल से तैर सकती है, यह दूरी को धारा के प्रवाह के अनुकूल तय करने में धारा के प्रतिकूल तय में लगे समय से 8 घंटे कम लेती है | धारा की चाल ज्ञात कीजिये |

  1. 4 kmph/किमी./घंटा

  2. 3 kmph/किमी./घंटा

  3. 2 kmph/किमी./घंटा

  4. 5 kmph/किमी./घंटा
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let stream speed be x kmph. Downstream speed = 6 + x, upstream speed = 6 - x. Time downstream = 36/(6+x), time upstream = 36/(6-x). Given: 36/(6-x) - 36/(6+x) = 8. Multiplying by (6-x)(6+x): 36(6+x) - 36(6-x) = 8(36 - x²). This gives 36(6+x-6+x) = 8(36-x²), so 72x = 8(36-x²), or 9x = 36 - x². Rearranging: x² + 9x - 36 = 0, which gives (x+12)(x-3) = 0. Since speed can't be negative, x = 3 kmph.

Multiple choice

In an hour a boat goes 18 km. along the stream and 12 km. in still water. What is the speed of boat against the streem? एक घन्टे में एक नाव धारा के साथ 18 किमी. तथा शान्त जल में 12 किमी. जाती है। धारा के विपरीत नाव की चाल क्या होगी?

  1. 6 km./hr./किमी./घं.

  2. 8 km./hr./किमी./घं.

  3. 12 km./hr./किमी./घं.

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

Speed in still water = 12 km/hr. Downstream speed = 18 km/hr. Speed of stream = downstream - still water = 18 - 12 = 6 km/hr. Upstream speed (against stream) = still water - stream speed = 12 - 6 = 6 km/hr.

Multiple choice

The speed of current is 4 kmph. A boat takes the same time in going 20 km downstream while as it goes 12 km upstream. Find the speed of the boat. धारा की चाल 4 किमी./घंटा है | एक नाव 20 किमी. धारा के अनुप्रवाह जाने में समान समय लेती है जितना कि 12 किमी. ऊर्ध्वप्रवाह जाने में लेती है | नाव की चाल ज्ञात कीजिये |

  1. 12 kmph (किमी./घंटा)

  2. 15 kmph (किमी./घंटा)

  3. 16 kmph (किमी./घंटा)

  4. 10 kmph (किमी./घंटा)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = b. Downstream speed = b+4, upstream = b-4. Times are equal: 20/(b+4) = 12/(b-4). Cross-multiplying: 20b - 80 = 12b + 48, giving 8b = 128, so b = 16 kmph. Option B (15) would not satisfy the time equality condition.

Multiple choice

The speed of a boat in still water is 16 kmph.It can travel some distance downstream in the same time as it can travel upstream which is 60% of the distance downstream, then find the total distance covered by boat including upstream and downstream. It is given that speed of current is 4 kmph and time for going upstream is 1 hr.- एक नाव की स्थिर जल में चाल 16 किमी./घण्टा है। यह धारा के अनुकूल किसी दूरी को समान समय में तय करती है जितना कि धारा के प्रतिकूल तय करती है जो धारा के अनुकूल चली दूरी का 60% है। तो नाव द्वारा धारा के अनुकूल और धारा के प्रतिकूल तय की गई दोनों दूरियों का योग ज्ञात कीजिए यदि यह ज्ञात है कि धारा की चाल 4 किमी./घण्टा है और धारा के अनुप्रवाह जाने में लगा समय 1 घण्टा है।

  1. 20

  2. 30

  3. 40

  4. 50
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed in still water = 16 kmph, current speed = 4 kmph. Downstream speed = 16+4 = 20 kmph. Upstream speed = 16-4 = 12 kmph. Let downstream distance = D. Then upstream distance = 0.6D. Time upstream = time downstream = 1 hour. So D = 20 km and 0.6D = 12 km. Total distance = D + 0.6D = 1.6D = 40 km. The key insight is recognizing the 60% relationship and using time = 1 hour.

Multiple choice

Speed of a boat is 5 km per hour in still water and the speed of the stream is 3 km per hour. If the boat takes 3 hours to go to a place and come back, the distance of the place is - स्थिर जल में एक नौका की चाल 5 किमी/घंटा है और धारा की चाल 3 किमी/घंटा है। यदि नौका को एक स्थान पर जाने और वापस आने में 3 घंटे लगते हैं तो उस स्थान की दूरी है -

  1. 3.75 km./किमी.

  2. 4 km./किमी.

  3. 4.8 km./किमी.

  4. 4.25 km./किमी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Boat speed in still water = 5 km/h, stream speed = 3 km/h. Downstream speed = 5 + 3 = 8 km/h. Upstream speed = 5 - 3 = 2 km/h. If distance is d km and total time is 3 hours: d/8 + d/2 = 3. Multiplying by 8: d + 4d = 24, so 5d = 24, giving d = 24/5 = 4.8 km. Therefore, the place is 4.8 km away.