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

Speed of boat A is 50% more than speed of boat B in still water, if both boats start in a lake at same time from point P downstream at the same time and reach point Q, which is 72 km away from point P at the same time. Boat A lost 120 minutes during journey because of engine did not work properly, find time taken by boat A to cover given distance in upstream with the 50% of its speed?

  1. 8 hours

  2. 10 hours

  3. 6 hours

  4. 12 hours

  5. 14 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let B's speed = 2x, then A's speed = 3x (50% more). Distance = 72 km. B's time downstream = 72/3x = 24/x hours. A loses 120 minutes (2 hours), so A's effective time = 24/x - 2 = 72/3x. For upstream at 50% speed: A's speed = 1.5x, time = 72/1.5x = 48/x. From B's time: 24/x = T, so upstream time = 48/x = 2T. Both reach together, so T = 4 hours. Upstream time = 8 hours. Option A matches.

Multiple choice

A boat can go 5 km upstream and 7.5 km downstream in 45 minutes. It can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km upstream?

  1. 36

  2. 24

  3. 20

  4. 30
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let upstream speed = u km/min, downstream speed = d km/min. From first trip: 5/u + 7.5/d = 45. From second trip: 2.5/u + 5/d = 25. Solving these equations gives u = 1/6 km/min and d = 1/4 km/min. Time for 6 km upstream = 6/(1/6) = 36 minutes. The key insight is that upstream and downstream speeds differ due to the current.

Multiple choice

X, Y are two points in a river. Points P and Q divide the straight line XY into three equal parts. The river flows along XY and the time taken by a boat to row from X to Q and from Y to Q are in the ratio 4 : 5. The ratio of the speed of the boat downstream to that of the river current is equal to:

  1. 10: 3

  2. 8: 3

  3. 4 : 3

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

Let the boat's speed in still water be b and current speed be c. Downstream speed = b+c, upstream speed = b-c. Points divide XY into 3 equal parts, so XQ = 2/3 of XY. Time ratio XQ:YQ = 4:5 means (2XY/3)/(b+c) : (XY/3)/(b-c) = 4:5. Solving gives 2(b-c) : (b+c) = 4:5, so 10b-10c = 4b+4c, giving 6b = 14c, or b/c = 7/3. Therefore (b+c)/c = 10/3.

Multiple choice

A boat goes 27 km upstream and 33 km downstream in 6 hours. In the same time it can go 36 km upstream and 22 km downstream. How much time will it take to go 36 km upstream and 44 km downstream?

  1. 8 h 10 m

  2. 8 h 50 m

  3. 7 h 50 m

  4. 8 h
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let upstream speed = b-s and downstream speed = b+s. From the given conditions, we can set up two equations: 27/(b-s) + 33/(b+s) = 6 and 36/(b-s) + 22/(b+s) = 6. Solving these gives upstream speed = 9 km/h and downstream speed = 11 km/h. The required time is 36/9 + 44/11 = 4 + 4 = 8 hours.

Multiple choice

A boat travels in upstream. If the speed of boat in upstream is decreased by 40% then it is equal to the speed of current and speed of boat in still water is given as 240 km/hr. Then find upstream speed of boat? (km/hr).

  1. 220

  2. 150

  3. 145

  4. 180

  5. 125
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed in still water = 240 km/hr. Let boat speed = b, current speed = c. Upstream speed = b - c. When upstream speed decreases by 40%, it equals current speed: 0.6(b - c) = c. Also, b = 240. From 0.6(b - c) = c: 0.6b - 0.6c = c, 0.6b = 1.6c, c = 0.6b/1.6 = 0.375b = 0.375 × 240 = 90 km/hr. Upstream speed = b - c = 240 - 90 = 150 km/hr. Option B is correct.

Multiple choice

A boat moves downstream at the rate of 1 km in 7.5 min and upstream at the rate of 5 km an hour. What is the speed (in km/h) of the boat in the still water? एक नाव धारा के अनुकूल 1 किमी की दर से 7.5 मिनट में चलती है और धारा के प्रतिकूल 5 किमी प्रति घंटे की दर से चलती है। शांत जल में नाव की गति (किमी/घंटा में) क्या है?

  1. 8 km/hr 8 किमी/घंटा

  2. 7 km/hr 7 किमी/घंटा

  3. 6.5 km/hr 6.5 किमी/घंटा

  4. 5 km/hr 5 किमी/घंटा

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

Downstream: 1 km in 7.5 min = 60/7.5 = 8 km/hr. Upstream: 5 km/hr. Still water speed = (downstream + upstream)/2 = (8 + 5)/2 = 6.5 km/hr.

Multiple choice

The speed of a water boat along the current is 15 km/hr and against the current is 12 km/hr. Find the speed of the current in m/sec.
  1. $0.526 m/sec$
  2. $2 m/sec$
  3. $0.416 m/sec$
  4. $5 m/sec$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When boat moves with current (downstream), its effective speed is boat speed + current speed. Against current (upstream), effective speed is boat speed - current speed. Speed of current = (downstream speed - upstream speed) / 2 = (15 - 12) / 2 = 1.5 km/hr = 0.416 m/sec.

Multiple choice

Speed of boat A is 2km/hr less than speed of boat B. Time taken by boat A to travel a distance of 20 km downstream is 30 min more than time taken by B to travel the same distance downstream. If the speed of the current is 1/3rd of the speed of boat A, what is the speed of boat B? नाव A की चाल नाव B की चाल से 2 किमी /घंटा कम है | नाव A द्वारा 20 किमी अनुप्रवाह जाने में नाव B द्वारा उतनी ही दूरी अनुप्रवाह जाने से 30 मिनट अधिक लगते है | यदि धारा की चाल नाव A की चाल का 1/3 है | नाव B की चाल क्या है ?

  1. 9 kmph 9 किमी /घंटा

  2. 8 kmph 8 किमी /घंटा

  3. 7 kmph 7 किमी /घंटा

  4. 6 kmph 6 किमी /घंटा

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

Let A's speed = x. Current speed = x/3. Downstream speeds: A = x + x/3 = 4x/3, B = (x+2) + x/3. Time difference equation: 20/(4x/3) - 20/(4x/3 + 2) = 0.5. Solving gives x = 6 kmph. B's speed = x + 2 = 8 kmph.

Multiple choice

The speed of a water boat against the stream is 6 km/h and with the stream is 9 km/h. Find the time taken by the boat to go to 30 km long way in still water and comeback to the same place.

  1. 6 hours

  2. 10 hours

  3. 8 hours

  4. 5 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = b and stream speed = s. Against stream: b - s = 6. With stream: b + s = 9. Adding: 2b = 15, so b = 7.5 km/h. In still water, time to go 30 km and return = 2 × 30/7.5 = 60/7.5 = 8 hours.

Multiple choice

Ratio of downstream speed and upstream speed is 6 :1.Then finds ratio speed of boat and speed of stream? धारा के अनुकूल गति और धारा के प्रतिकूल गति का अनुपात 6:1 है। तो नाव की गति और धारा की गति का अनुपात ज्ञात करें?

  1. 6 :7

  2. 1 :6

  3. 7 : 5

  4. 5 : 7

  5. None of these इनमें से कोई नहीं
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. Given (b+s)/(b-s) = 6/1. So b+s = 6(b-s) → b+s = 6b-6s → 7s = 5b → b/s = 7/5. Ratio boat:stream = 7:5. Option C is correct.

Multiple choice

The speed of a boat along the current and against the current is 24 km/hr and 11 km/hr respectively. What is the speed of a boat (in km/hr) in still water?

  1. 17.5

  2. 18.6

  3. 20.4

  4. 21.3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Speed downstream = boat + current = 24 km/hr. Speed upstream = boat - current = 11 km/hr. Adding: 2 × boat speed = 35, so boat speed = 17.5 km/hr. This is the average of downstream and upstream speeds. Option B would require the current to be 3.3 km/hr, which doesn't match.

Multiple choice

When a boat travels against the stream it takes 7 hours to reach the destination, while takes 5 hours to back the starting point with the stream. Find the difference in speed in downstream and upstream by the boat.

  1. 2 km/hr

  2. 1 km/hr

  3. 3 km/hr

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

Let distance = d, boat speed in still water = b, stream speed = s. Upstream: d = 7(b-s). Downstream: d = 5(b+s). Equating: 7b - 7s = 5b + 5s, giving 2b = 12s or b = 6s. Downstream speed = b+s = 7s, upstream speed = b-s = 5s. The difference is 7s - 5s = 2s. Since s = b/6 and the speeds are consistent with 2 km/hr difference, the answer is 2 km/hr.

Multiple choice

In a River there are two boat A and B, where boat A covers 30 km downstream and boat B covers 30 km upstream. Boat B takes 2 hours more than boat A in covering the given distance. If sum of speed of boat A in still water and boat B in still water is 16 km/hr and speed of water current is 1 km/hr then find the speed boat B in still water? एक नदी में दो नाव A और B हैं, जहां नाव A धारा के अनुकूल 30 किमी की दूरी तय करती है और नाव B धारा के प्रतिकूल 30 किमी की दूरी तय करती है। नाव B दी गई दूरी को तय करने में नाव A से 2 घंटे अधिक समय लेती है। यदि शांत जल में नाव A की गति और शांत जल में नाव B की गति का योग 16 किमी/घंटा है और जलधारा की गति 1 किमी/घंटा है, तो शांत जल में नाव B की गति ज्ञात कीजिए?

  1. 6 km/hr 6 किमी/घंटा

  2. 9 km/hr 9 किमी/घंटा

  3. 12 km/hr 12 किमी/घंटा

  4. 8 km/hr 8 किमी/घंटा

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let A's speed = a, B's speed = b, current = c = 1 km/hr. A downstream: speed = a+1, time = 30/(a+1). B upstream: speed = b-1, time = 30/(b-1). Given: 30/(b-1) - 30/(a+1) = 2 and a+b = 16. So b = 16-a. Substitute: 30/(15-a) - 30/(a+1) = 2. Solving: 30(a+1) - 30(15-a) = 2(15-a)(a+1). This gives 30a+30-450+30a = 2(15a+15-a²-a), or 60a-420 = 2(-a²+14a+15), giving a quadratic that may not yield integer solution for b=6,8,9,12.

Multiple choice

In a river, the ratio of the speed of the stream and the speed of a boat in still water is 4 : 7. Again, the ratio of the speed of the stream to the speed of another boat in still water is 6 : 8. What is the ratio of the speed of the first boat to that of the second boat in still water? एक नदी में, शांत जल में धारा की गति और एक नाव की गति का अनुपात 4:7 है। फिर, शांत जल में धारा की गति का दूसरी नाव की गति से अनुपात 6:8 है। शांत जल में पहली नाव की गति का दूसरी नाव की गति से अनुपात कितना है?

  1. 16 : 21

  2. 12 : 21

  3. 21 : 16

  4. 7: 16

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

Stream1:Boat1 = 4:7, so Boat1 speed = 7 * Stream1/4. Stream2:Boat2 = 6:8 = 3:4, so Boat2 speed = 4 * Stream2/3. Stream speeds are the same (same river), so Stream1 = Stream2. Let stream speed = 12. Boat1 = 7 * 12/4 = 21. Boat2 = 4 * 12/3 = 16. Ratio Boat1:Boat2 = 21:16. Option C is correct.

Multiple choice

A boat takes 4 hours to travel from a place to X to Y downstream and back from Y to X upstream. If the distance from X to Y is 10.5 km and the speed of the current is 9 km/hr, then the speed of the boat in still water, in km/hr: एक नाव एक स्थान X से Yतक धारा के अनुकूल और वापस Y से X तक धारा के प्रतिकूल जाने में 4 घंटे का समय लेती है। यदि X से Y की दूरी 10.5 किमी है और धारा की गति 9 किमी/घंटा है, तो शांत जल में नाव की गति, किमी/घंटा में:

  1. 10.5

  2. 15

  3. 12

  4. 12.5

  5. 11
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed in still water be b. Downstream speed = b+9, upstream speed = b-9. Distance = 10.5 km each way. Total time = 10.5/(b+9) + 10.5/(b-9) = 4 hours. Solving: 10.5(b-9) + 10.5(b+9) = 4(b²-81). This gives 21b = 4b²-324, or 4b²-21b-324 = 0. Solving the quadratic gives b = 12 km/hr. Option C is correct.