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 travels 48 km upstream in 12 h and 40 km downstream in 8 h. Then, the speed of a boat in still water and the speed of current are respectively.
  1. $3.5, 1.5$
  2. $4, 1$
  3. $4.5, 0.5$
  4. $2.5, 2.5$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Upstream speed = boat - current = 48/12 = 4 km/h. Downstream speed = boat + current = 40/8 = 5 km/h. Adding: 2 × boat = 9, so boat = 4.5 km/h. Subtracting: 2 × current = 1, so current = 0.5 km/h. This uses the standard formula for relative speed in flowing water.

Multiple choice

Speed of a boat along the current and against the current is 32 km/hr and 20 km/hr respectively. What is the speed of the current?

  1. 2 km/hr

  2. 3 km/hr

  3. 4 km/hr

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

If boat speed in still water is b and current speed is c: b + c = 32 (downstream) and b - c = 20 (upstream). Subtracting: (b+c) - (b-c) = 32-20, so 2c = 12, thus c = 6 km/hr. The current speed is half the difference between downstream and upstream speeds.

Multiple choice

A boat runs at 22 km per hour along the stream and 10 km per hour against the stream. Find the ratio of speed of the boat in still water to that of the speed of the stream.
  1. $8: 3$
  2. $3: 5$
  3. $5: 3$
  4. $3: 8$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let boat speed in still water = b, stream speed = s. Downstream speed = b + s = 22. Upstream speed = b - s = 10. Adding: 2b = 32, so b = 16 km/h. Subtracting: 2s = 12, so s = 6 km/h. Ratio b:s = 16:6 = 8:3.

Multiple choice

A boat can travels 15km downstream in 18 min. The ratio of the boat in still water to speed of stream is 4:1. How much time will the boat take to cover 10km upstream?

  1. 22 minutes

  2. 25 minutes

  3. 20 minutes

  4. 30 minutes

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

Downstream speed = 15 km / (18/60) hr = 50 km/h. Boat speed : stream speed = 4:1, so boat speed = 40 km/h, stream speed = 10 km/h. Upstream speed = 40 - 10 = 30 km/h. Time for 10 km upstream = 10/30 hr = 20 minutes.

Multiple choice

Find the values and state the correct relationship. मान ज्ञात कीजिये तथा सही सम्बन्ध स्थापित कीजिये। The speed of boat in still water is 4 kmph more than the speed of stream. The sum of distance covered by boat in 2 hours upstream and 2 hours downstream is 28 km. Quantity I: Distance travelled by boat downstream in 5 hours. Quantity II: Average speed of Siddharth while driving a car from home to office and back when travelling at a speed of 50 kmph from home to office and at a speed of 40 kmph from office to home. शांत जल में नाव की गति धारा की गति से 4 किमी/घंटे अधिक है। 2 घंटे ऊर्ध्वंप्रवाह और 2 घंटे अनुप्रवाह में नाव द्वारा चली गयी दूरी 28 किमी है। मात्रा I: नाव द्वारा 5 घंटे में अनुप्रवाह में चली गयी दूरी । मात्रा II: घर से कार्यालय तक 50 किमी प्रति घंटे की चाल से यात्रा करते समय और कार्यालय से घर तक 40 किमी प्रति घंटे की रफ्तार से यात्रा करते समय सिद्धार्थ की औसत गति ।

  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity II > Quantity I मात्रा II > मात्रा I

  4. Quantity II ≥ Quantity I मात्रा II ≥ मात्रा I

  5. Quantity I = Quantity II or Relation cannot be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता है।
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let stream speed=x, boat speed=4+x. Upstream distance=2(4+x-x)=8 km. Downstream distance in 2h=28-8=20 km, so 2(4+2x)=20 gives 4+2x=10, x=3 kmph. Boat speed=7 kmph. Quantity I: Downstream distance in 5h=5×10=50 km. Quantity II: Average speed=2×50×40/(50+40)=4000/90≈44.44 kmph. Since 50 > 44.44, Quantity I is greater.

Multiple choice

A boat takes 6 hrs to travel 144 km downstream . The speed of the boat downstream is 1.5 times of the speed of the boat upstream . What is the speed of the current ? (in kmph) एक नाव को 144 किमी अनुप्रवाह यात्रा करने में 6 घंटे लगते हैं। नाव के अनुप्रवाह की गति, नाव के उर्ध्प्रवाह की गति का 1.5 गुना है। धारा की गति क्या है ? ( किमी / घ में )

  1. 4 km / hrs 4 किमी / घ

  2. 20 km / hrs 20 किमी / घ

  3. 6 km / hrs 6 किमी / घ

  4. 18 km / hrs 18 किमी / घ

  5. None of these इनमे से कोई नही
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Downstream speed = 144/6 = 24 km/h. Upstream speed = 24/1.5 = 16 km/h. Speed of current = (downstream - upstream)/2 = (24-16)/2 = 4 km/h. Option A is correct.

Multiple choice

A boat takes 40 minutes less to travel 10 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 8 km/hr then the speed of the stream is एक नाव 10 किमी धारा के अनुप्रवाह जाने में , समान दूरी में धारा के प्रतिकूल जाने की तुलना में 40 कम समय लेती है। यदि शान्त जल में नाव की चाल 8 किमी/घंटा है तो धारा की चाल क्या होगी ?

  1. 2 km/hr 2 किमी / घंटा

  2. 5 km/hr 5 किमी / घंटा

  3. 9 km/hr 9 किमी / घंटा

  4. 12 km/hr 12 किमी / घंटा

  5. 15 km/hr 15 किमी / घंटा
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let stream speed be x km/hr. Downstream speed = 8+x, upstream speed = 8-x. Time difference: 40 minutes = 2/3 hour. Time upstream - Time downstream = 2/3. So 10/(8-x) - 10/(8+x) = 2/3. Simplifying: 10(8+x) - 10(8-x) = (2/3)(8-x)(8+x). 10(8+x-8+x) = (2/3)(64-x²). 20x = (2/3)(64-x²). 30x = 64 - x². x² + 30x - 64 = 0. (x+32)(x-2) = 0. x = 2 or x = -32. Speed can't be negative, so x = 2 km/hr.

Multiple choice

Eng A boat can cover X km while going down upstream in same time in which it can cover (X-8) km while going up stream. If the difference between the distance covered in 1 hr. Downstream and upstream is 6 km and speed of boat in still water is 15 km/hr, then find the value of X. एक नाव X किमी. की दूरी तय कर सकती है जब यह धारा के अनुप्रवाह जाती है और यह समान समय में (X-8) किमी. की दूरी तय कर सकती है जब यह धारा के ऊर्ध्वप्रवाह जाती है। यदि 1 घंटे में अनुप्रवाह और ऊर्ध्वप्रवाह तय की गयी दूरियों में 6 किमी. का अन्तर है और स्थिर जल में नाव की चाल 15 किमी./घंटा है, तो X का मान ज्ञात कीजिए।

  1. 18 Km

  2. 24 Km

  3. 30 Km

  4. 15 Km

  5. Can not be determined निर्धारित नहीं किया जा सकता है
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let stream speed = s km/hr. Downstream speed = 15 + s, upstream speed = 15 - s. In 1 hour, downstream covers (15 + s) km and upstream covers (15 - s) km. Distance difference = (15 + s) - (15 - s) = 2s = 6 km, so s = 3 km/hr. Time to cover X km downstream = X/(15 + 3) = X/18 hours. Time to cover (X-8) km upstream = (X-8)/(15-3) = (X-8)/12 hours. Since times are equal: X/18 = (X-8)/12. Cross-multiplying: 12X = 18(X-8), giving 12X = 18X - 144, so 6X = 144 and X = 24.

Multiple choice

Upstream speed is 6 km/hr less than the downstream speed. The speed of the boat is 21 km/hr. Find the time (in hour) to cover the distance of 108 km in the upstream. उर्ध्वप्रवाह चाल अनुप्रवाह चाल से 6 किमी / घंटा कम है। नाव की गति 21 किमी / घंटा है। उर्ध्वप्रवाह में 108 किमी की दूरी तय करने के लिए समय (घंटे में) ज्ञात करें?

  1. 7

  2. 11

  3. 6

  4. 9

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

Let stream speed = x km/hr. Then downstream speed = 21 + x and upstream speed = 21 - x. Given: (21 + x) - (21 - x) = 6 → 2x = 6 → x = 3 km/hr. Upstream speed = 21 - 3 = 18 km/hr. Time to cover 108 km upstream = 108/18 = 6 hours. Option C is correct.

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? नाव A की गति शांत जल में नाव B की गति से 50% अधिक है, यदि दोनों नाव एक झील में एक ही समय में एक बिंदु P से अनुप्रवाह से शुरू होती हैं और बिंदु Q तक पहुंचती हैं, जो एक ही समय पर बिंदु P से 72 किमी दूर है। नाव A यात्रा के दौरान 120 मिनट खराब कर देता है क्योंकि इंजन ठीक से काम नहीं कर रहा था, तो नाव A द्वारा दी गई दूरी को अपनी गति के 50% के साथ धारा की विपरीत दिशा में तय करने में लगा समय ज्ञात कीजिए?

  1. 8 hours/घंटा

  2. 10 hours/घंटा

  3. 6 hours/घंटा

  4. 12 hours/घंटा

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

Let boat B's speed be v km/h. Then boat A's speed = 1.5v (50% more). Since A loses 120 minutes (2 hours) but both reach together: 72/v = 72/(1.5v) + 2. Solving: 72/v = 48/v + 2, so 24/v = 2, giving v = 12 km/h. Therefore A's speed = 18 km/h. At 50% of this speed (9 km/h) for 72 km upstream: time = 72/9 = 8 hours. The downstream context establishes the speeds; upstream uses the reduced speed.

Multiple choice

A boat can cover 20 km upstream and 32 km downstream together in 3 hours. Also it can cover 40 km upstream and 48 km downstream together in 5.5 hours. What is the speed of the current (in km/h)? एक नाव 3 घंटे में 20 किमी उर्ध्वप्रवाह की ओर और 32 किमी अनुप्रवाह की ओर एक साथ जा सकती है। साथ ही यह 5.5 घंटे में 40 किमी उर्ध्वप्रवाह की ओर और 48 किमी अनुप्रवाह की ओर तय कर सकती है। धारा की गति (किमी / घंटा में) ज्ञात कीजिए?

  1. 13

  2. 8

  3. 7

  4. 11

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

Let boat speed = b, current speed = c. Upstream speed = b - c, downstream = b + c. Equation 1: 20/(b-c) + 32/(b+c) = 3. Equation 2: 40/(b-c) + 48/(b+c) = 5.5. Multiply eq1 by 2: 40/(b-c) + 64/(b+c) = 6. Subtract eq2 from this: 16/(b+c) = 0.5, so b+c = 32. From eq1: 20/(b-c) = 3 - 32/32 = 2, so b-c = 10. Thus c = (32-10)/2 = 11 km/h.

Multiple choice

The speed of boat when travelling downstream is 32 km/h, whereas when travelling upstream it is 28 km/h. What is the speed of the boat in still water? धारा के साथ यात्रा करते समय नाव की गति 32 किमी / घंटा है, जबकि धारा के विपरीत यात्रा करते समय यह 28 किमी / घंटा है। स्थिर जल में नाव की गति ज्ञात कीजिये?

  1. 28

  2. 32

  3. 30

  4. 34

  5. 35
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = b and stream speed = s. Downstream: b + s = 32, upstream: b - s = 28. Adding the equations gives 2b = 60, so b = 30 km/h. The answer is neither 28 (downstream speed) nor 32 (upstream speed).

Multiple choice

There are two quantities provided in the following questions. You have to find out the values of the quantities and compare them according to the given codes as follows: Quantity I: Speed of boat in still water, if a man can travel 54 km downstream in 9 hours and 40 km upstream in 10 hours. Quantity II: Speed of boat in still water, if a man can travel 45 km downstream in 9 hours and the speed of stream is 1 kmph.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or the relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Downstream speed = 54/9 = 6 kmph, upstream speed = 40/10 = 4 kmph. Boat speed = (downstream + upstream)/2 = (6+4)/2 = 5 kmph. Quantity II: Downstream speed = 45/9 = 5 kmph, stream speed = 1 kmph. Boat speed = downstream speed - stream speed = 5 - 1 = 4 kmph. Since 5 > 4, Quantity I > Quantity II.