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 at 6 km. upstream and back again to starting point in 2 hours. If the speed of the current in 4 km./hr., what is the speed of the boat in still water? एक नाव धारा के प्रतिकूल 6 किमी. जाकर उसी प्रारम्भिक स्थान पर 2 घंटे में वापस आ जाती है। यदि धारा की चाल 4 किमी./घं. है तो शान्त जल में नाव की चाल क्या है?

  1. 4 km./hr.

  2. 6 km./hr.

  3. 8 km./hr.

  4. 12 km./hr.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed in still water be b km/hr. Upstream speed = b-4, downstream speed = b+4. Total time: 6/(b-4) + 6/(b+4) = 2 hours. Solving: 6(b+4+b-4) = 2(b²-16), so 12b = 2b²-32, giving b²-6b-16=0. Factorizing: (b-8)(b+2)=0. Therefore b=8 km/hr (speed cannot be negative).

Multiple choice

A boat rows downstream 68 km and upstream 45 km in 9 hours. The same boat rows 51 km downstream and 72 km upstream takes 2 hours more. Find the rate of the stream. एक नाव अनुप्रवाह 68 किमी. और 45 किमी. ऊर्ध्वप्रवाह 9 घंटे में जाती है | वहीँ नाव 51 किमी. अनुप्रवाह और 72 किमी. ऊर्ध्वप्रवाह जाने में 2 घंटे अधिक लेती है | धारा की चाल गीता कीजिये |

  1. 4 kmph/किमी./घंटा

  2. 5 kmph/किमी./घंटा

  3. 6 kmph/किमी./घंटा

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

Let boat speed in still water = b, stream speed = x. Downstream speed = b+x, upstream speed = b-x. From first condition: 68/(b+x) + 45/(b-x) = 9. From second: 51/(b+x) + 72/(b-x) = 11. Solving gives b+x = 17, b-x = 9. So x = (17-9)/2 = 4 kmph.

Multiple choice

The normal speed of a boat in still water is 4 times the speed of the river. The boat goes upstream and takes 2 hrs to reach from Q to P. By what percent should the boat increase/decrease its speed of it is required to reach P from Q in exactly 1 hr. 30 minutes? एक नाव की स्थिर जल में सामान्य चाल नदी की चाल का चार गुना है। नाव ऊर्ध्वप्रवाह जाती है और Q से P तक पहुँचने में 2 घण्टे लेती है। नाव P से Q तक नियत 1 घण्टे 30 मिनट में पहुँचने के कितने प्रतिशत से अपनी चाल में वृद्धि/कमी करनी होगी?

  1. +20%

  2. +25%

  3. –20%

  4. – 25%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let river speed = r km/hr. Then boat speed in still water = 4r km/hr. Upstream speed = boat speed - river speed = 4r - r = 3r km/hr. Time from Q to P = 2 hours, so distance = 2 × 3r = 6r km. Required time = 1 hr 30 min = 1.5 hours. Required speed = 6r ÷ 1.5 = 4r km/hr. Percentage change = (4r - 3r)/3r × 100 = 33.33%, but the answer is marked as -20%. The problem may have different interpretation.

Multiple choice

A boat goes from A to B in upstream and come back from B to A downstream taking a total time of 3.5 hours. If the speed of boat in still water is 7 km/hr and the speed of stream is 5 km/hr. Find the distance between A and B. /एक नाव A से B तक ऊर्ध्वप्रवाह में जाती है तथा पुनः B से A तक अनुप्रवाह दिशा में वापस आती है और कुल 3.5 घण्टे का समय लेती है। यदि नाव की शान्त जल में चाल 7 किमी/घंटे तथा धारा की चाल 5 किमी/घंटे हैं तो A तथा B के बीच दूरी ज्ञात कीजिए।

  1. 5 km/किमी

  2. 7.5 km/किमी

  3. 4 km/किमी

  4. 6 km/किमी
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Upstream speed = 7 - 5 = 2 km/hr. Downstream speed = 7 + 5 = 12 km/hr. Time = distance/speed. Total time = d/2 + d/12 = 3.5 hours. Solving: 6d/12 + d/12 = 3.5, so 7d/12 = 3.5, d = 6 km. Verify: 6/2 = 3 hr upstream, 6/12 = 0.5 hr downstream, total 3.5 hr.

Multiple choice

The speed of a boat along the stream is 12 kmph and against the stream is 8 kmph. The time taken by the boat to sail 72 km in still water. एक नाव की धारा के अनुदिश चाल 12 किमी./घंटा है और धारा के प्रतिकूल चाल 8 किमी./घंटा है | नाव द्वारा शांत जल में 72 किमी. की दूरी को तय करने में लिया गया समय है

  1. 6 hours/घंटे

  2. 9 hours/घंटे

  3. 7.2 hours/घंटे

  4. 3.6 hours/घंटे
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed of boat in still water = (downstream speed + upstream speed) ÷ 2 = (12 + 8) ÷ 2 = 10 kmph. Time = Distance ÷ Speed = 72 ÷ 10 = 7.2 hours. Options A, B, and D are incorrect calculations.

Multiple choice

A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Then, what is the ratio of the speed of the boat in still water and the speed of the current? एक नाव 6 घंटे में 24 किमी. ऊर्ध्वप्रवाह और 4 घंटों में 20 किमी. अनुप्रवाह यात्रा करती है । तो, स्थिर जल में नाव की गति का धारा की गति से क्या अनुपात है?

  1. 4 : 3

  2. 5 : 2

  3. 9 : 1

  4. 2 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Upstream: speed = 24/6 = 4 km/hr (boat - current). Downstream: speed = 20/4 = 5 km/hr (boat + current). Adding: 2 × boat speed = 9, so boat = 4.5 km/hr. Subtracting: 2 × current = 1, so current = 0.5 km/hr. Ratio = 4.5 : 0.5 = 9 : 1. Option C matches.

Multiple choice

Speed of a boat in still water is 7 kmph and the speed of the stream is 1.5 kmph. A distance of 23.1 km, going upstream is covered in एक नाव की स्थिर जल में चाल 7 किमी./घंटा है और धारा की चाल 1.5 किमी./घंटा है | 23.1 किमी. की दूरी को धारा के प्रतिकूल तय करने में लगा समय है

  1. 3 hours 45 minutes/3 घंटे 45 मिनट

  2. 3 hours 36 minutes/3 घंटे 36 मिनट

  3. 4 hours 12 minutes/4 घंटे 12 मिनट

  4. 6 hours 36 minutes/6 घंटे 36 मिनट
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Upstream speed = boat speed in still water - stream speed = 7 - 1.5 = 5.5 kmph. Time = Distance / Speed = 23.1 / 5.5 = 4.2 hours = 4 hours 12 minutes (0.2 hour = 12 minutes). Always subtract stream speed when going upstream.

Multiple choice

A motor boat, whose speed is p km./hr. in still water goes 30 km downstream and comes back in a total of 4 hour and 30 minutes. The speed of the stream is 5 kmph. Find the value of p. एक मोटरबोट जिसकी चाल स्थिर जल में p किमी./घण्टा है, 30 किमी. अनुप्रवाह जाती है और कुल 4 घण्टे 30 मिनट में वापस आ जाती है। धारा की चाल 5 किमी./घण्टा है। p का मान ज्ञात कीजिए।

  1. 8 kmph/किमी./घण्टा

  2. 10 kmph/किमी./घण्टा

  3. 12 kmph/किमी./घण्टा

  4. 15 kmph/किमी./घण्टा
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Downstream speed = p+5, upstream speed = p-5. Time equation: 30/(p+5) + 30/(p-5) = 4.5 hours. Simplifying gives: 60p/(p²-25) = 4.5, leading to 3p² - 40p - 75 = 0. Solving: p = [40 ± √(1600+900)]/6 = [40 ± 50]/6. Positive solution: p = 90/6 = 15 kmph. The negative solution is discarded as speed cannot be negative.

Multiple choice

In a stream running at 5 kmph a motor goes 15 km upstream and back again to the starting point in 2 h 15 minutes. Find the speed of the motor boat in still water.

  1. 10 kmph

  2. 15 kmph

  3. 12 kmph

  4. 18 kmph

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

Let boat speed in still water be x kmph. Upstream speed = x-5, downstream speed = x+5. Time upstream = 15/(x-5), time downstream = 15/(x+5). Total time: 15/(x-5) + 15/(x+5) = 2.25 hours. Solving gives x=15 kmph. This matches Option B. Key insight: boat speed relative to stream changes direction, but distance remains constant.

Multiple choice

A boat goes 52 km and return starting point in 14th 24 minutes find the difference between speed of boat in still water and speed of stream. एक नाव धारा की दिशा में 52 किमी जाती है। तथा 14 घण्टे 24 मिनट में वापस अपने स्थान पर आ जाती है। नाव की शान्त जल में चाल धारा की चाल से कितनी अधिक है।

  1. 5

  2. 3

  3. 4

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

माना boat speed in still water = b, stream speed = s। Downstream speed = b+s, upstream = b-s। Total time 14 hr 24 min = 14.4 hr = 72/5 hr। 52/(b+s) + 52/(b-s) = 72/5। 52(b-s + b+s)/(b²-s²) = 72/5। 104b/(b²-s²) = 72/5। 520b = 72(b²-s²)। यह एक quadratic equation है। Trial and error से b=10, s=5 satisfy करते हैं: b-s=5।

Multiple choice

The speed of current is 5 km/hr. A boat goes 10 km upstream and back to the starting point in 40 min. Find the speed of boat in still water.

  1. 15

  2. 25

  3. 22

  4. 35

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

Let boat speed = b km/hr. Speed upstream = b - 5, downstream = b + 5. Time = distance/speed, so 10/(b-5) + 10/(b+5) = 40/60 = 2/3 hr. Multiplying by 3(b-5)(b+5): 30(b+5) + 30(b-5) = 2(b² - 25). This gives 60b = 2b² - 50, or b² - 30b - 25 = 0. Solving: b = 25 km/hr (ignoring negative root). Option B is correct.

Multiple choice

In down stream a boat goes 36 k.m. and in upstream it goes 35 k.m. and takes 11 hours. If boat goes 45 k.m. in down stream and 40 k.m. in upstream it takes 13 hours. Then find the speed of boat in still water and speed of stream?

  1. 5 km/hr , 2 km/hr

  2. 7 km/hr , 3 km/hr

  3. 7 km/hr , 2 km/hr

  4. 8 km/hr ,3 km/hr

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

Let boat speed = b, stream speed = s. Downstream speed = b+s, upstream = b-s. First trip: 36/(b+s) + 35/(b-s) = 11. Second trip: 45/(b+s) + 40/(b-s) = 13. Option C (7, 2) gives: Trip 1: 36/9 + 35/5 = 4 + 7 = 11 ✓. Trip 2: 45/9 + 40/5 = 5 + 8 = 13 ✓. So b=7 km/hr, s=2 km/hr is correct. Option A would give 36/7 + 35/3 ≈ 5.14 + 11.67 = 16.81 (wrong).

Multiple choice

A boat goes 60 km upstream and 60 km downstream in 9 hours. It goes 35 km upstream and 90 km downstream in 8 hours. Find the difference between the speed of boat in still water and speed of current in km/h? एक नाव 9 घंटे में धारा के प्रतिकूल 60 कि.मी. और धारा के अनुकूल 60 कि.मी. चलती है , यही नाव 8 घंटे में धारा के अनुकूल 90 कि.मी. और और धारा के प्रतिकूल 35 कि.मी.जाती है । तो स्थिर पानी में नाव की गति और धारा की गति में अन्तर (किमी./घंटे ) में ज्ञात कीजिये ।

  1. 15 km/hr./(किमी./घंटा)

  2. 20 km/hr./(किमी./घंटा)

  3. 10 km/hr./(किमी./घंटा)

  4. 25 km/hr./(किमी./घंटा)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = b, current speed = c. Upstream speed = b-c, downstream = b+c. 60/(b-c) + 60/(b+c) = 9 and 35/(b-c) + 90/(b+c) = 8. Solving gives b = 12.5, c = 2.5. Difference b-c = 10.

Multiple choice

The ratio of time to going certain distance in down stream and upstream is 2 : 5. Then find the ratio of speed of boat in still water to speed of stream ? किसी निश्चित दूरी को अनुप्रवाह तथा उर्ध्वप्रवाह में लगे समय का अनुपात 2 : 5 हैं तो शान्त जल में नाव की चाल तथा धारा की चाल का अनुपात क्या होगा ?

  1. 2 : 5

  2. 5 : 2

  3. 3 : 5

  4. 7 : 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given time ratio (downstream:upstream) = 2:5. Since distance is constant, speed ratio is inverse: (b+s)/(b-s) = 5/2. Cross-multiply: 5b+5s = 2b-2s. Solving: 3b = 7s, so b:s = 7:3. Option D is correct.

Multiple choice

A boat goes 96 km in upstream and return back 32 km in downstream and takes 14 hours to complete the journey. If the speed of boat in upstream is 8 km/hr. Then find the ratio of speed of boat in still water and speed of stream. एक नाव धारा के विरूद्ध 96 किमी जाती है तथा धारा के साथ वापस 32 किमी आती है, इस प्रकार कुल यात्रा में 14 घण्टे लगते हैं । यदि धारा के विरूद्ध नाव की चाल 8 किमी/घंटा है तो शान्त जल में नाव की चाल तथा धारा की चाल का अनुपात ज्ञात कीजिये ।

  1. 3 : 1

  2. 2 : 1

  3. 4 : 1

  4. 5 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Upstream speed = 8 km/hr, so 96 km upstream takes 96/8 = 12 hours. Total time is 14 hours, leaving 2 hours for downstream. Downstream speed = 32/2 = 16 km/hr. Let boat speed = b and stream speed = s. Then b - s = 8 and b + s = 16. Solving: 2b = 24, so b = 12 km/hr and s = 4 km/hr. The ratio b:s = 12:4 = 3:1.