Boats and Streams Questions

Multiple choice
  1. $20 km/hr$
  2. $16 km/hr$
  3. $18 km/hr$
  4. $22 km/hr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed = b km/hr. Upstream speed = (b-4), downstream = (b+4). Total time = 80 minutes = 4/3 hours. So 10/(b-4) + 10/(b+4) = 4/3. Cross-multiply: 30(b+4) + 30(b-4) = 4(b²-16). This gives 60b = 4b² - 64, or 4b² - 60b - 64 = 0. Dividing by 4: b² - 15b - 16 = 0, giving (b-16)(b+1) = 0. Thus b = 16 km/hr. Option C (18) could result from sign errors in the quadratic.

Multiple choice
  1. 52.5 km 52.5 किमी

  2. 62.5km 62.5 किमी

  3. 55 km 55 किमी

  4. 58.7km 58.7 किमी

  5. None of these इनमें से कोई नहीं

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Downstream speed = 50/2 = 25 km/h. Upstream speed = 50/5 = 10 km/h. Boat speed = (25 + 10)/2 = 17.5 km/h. Distance in 3 hours in still water = 17.5 × 3 = 52.5 km. Option A is correct.

Multiple choice
  1. 63

  2. 84

  3. 82

  4. 81

  5. None of these इनमे से कोई नही|

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Downstream speed = 10 + 4 = 14 km/hr, upstream speed = 10 - 4 = 6 km/hr. If AB = d km, then C is at d/2 from A. Time downstream A to B = d/14 hr. Time upstream B to C = (d/2)/6 = d/12 hr. Total: d/14 + d/12 = 26 hr. d(13/84) = 26, so d = 26 × 84/13 = 84 km. Option B is correct.

Multiple choice
  1. 40 min 40 मिनट

  2. 44 min 44 मिनट

  3. 52 min 52 मिनट

  4. 59 min 59 मिनट

  5. 1 hour 4 min 1 घंटे 4 मिनट

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed in still water = 7x and stream speed = x. Upstream speed = 7x - x = 6x. Given: 4.2 km in 14 min, so upstream speed = 4.2/(14/60) = 18 km/hr. Therefore 6x = 18, x = 3 km/hr. Downstream speed = 7x + x = 8x = 24 km/hr. Time for 17.6 km = 17.6/24 hr = (17.6/24)*60 = 44 min.

Multiple choice
  1. 7

  2. 9

  3. 8

  4. 10

  5. 12

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed in still water = b km/h. Speed downstream = b + 3, speed upstream = b - 3. Time upstream = 2 × time downstream. If distance = d, then d/(b-3) = 2 × d/(b+3). Cross-multiplying: d(b+3) = 2d(b-3). Canceling d: b + 3 = 2b - 6. So: 3 + 6 = 2b - b, b = 9 km/h.

Multiple choice
  1. 3 hours 3 घंटे

  2. 8 hours 8 घंटे

  3. 10 hours 10 घंटे

  4. 13 hours 13 घंटे

  5. 15 hours 15 घंटे

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculate upstream speed (6 km/2 hr = 3 km/h) and downstream speed (8 km/0.5 hr = 16 km/h). Let boat speed = b and current speed = c. Then b - c = 3 and b + c = 16. Adding: 2b = 19, so b = 9.5 km/h. Time = 28.5/9.5 = 3 hours. Option A is correct.

Multiple choice
  1. 2 km/hr

  2. 3 km/hr

  3. 5 km/hr

  4. 6 km/hr

  5. 8 km/hr

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed = 10 km/hr, let current speed = c. Downstream speed = 10 + c, upstream speed = 10 - c. Time downstream = 91/(10 + c), time upstream = 91/(10 - c). Total time = 91/(10 + c) + 91/(10 - c) = 20. Testing c = 3: downstream speed = 13 km/hr (7 hours), upstream speed = 7 km/hr (13 hours), total = 20 hours. This satisfies the condition exactly. Other options don't satisfy the equation.

Multiple choice
  1. 4

  2. 4.5

  3. 5

  4. 5.5

  5. 10

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. From trip 1: 18/(b-s) + 14/(b+s) = 4. From trip 2: 3/(b-s) + 10.5/(b+s) = 1.25. Solving these equations gives s = 4 km/h. Option E (10) would be the boat speed, not stream speed.

Multiple choice
  1. I or II only केवल I या II

  2. II or III only केवल II या III

  3. II and (I or III) II तथा (I या III)

  4. Any one is sufficient कोई भी एक पर्याप्त है

  5. None of these इनमे से कोई नहीं

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The original information gives 24/(b-c) + 36/(b+c) = 6, where b is boat speed and c is current speed. Statement I gives b=10, so we have one equation in c. Statement II gives another equation 36/(b-c) + 24/(b+c) = 6.5; with the original, we have two equations in b and c. Statement III gives 48/(b-c)=6 and 48/(b+c)=4, directly yielding b-c=8 and b+c=12. Each statement alone (with original info) is sufficient.

Multiple choice
  1. 10 km/hr. 10 किमी/घंटा

  2. 13.50 km/hr. 13.50 किमी/घंटा

  3. 8.25 km/hr. 8.25 किमी/घंटा

  4. 14.50 km/hr. 14.50 किमी/घंटा

  5. None of these इनमे से कोई नहीं

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Upstream time is 25% more than downstream, so T_up = 1.25 × T_down. Since distance is same, speed is inversely proportional to time: S_up = S_down / 1.25. Also S_down = B + S, S_up = B - S where B=boat speed, S=stream speed. B - S = (B + S) / 1.25 gives B = 9S/1. Downstream speed = 375m / 90s = 15 km/hr. So B + S = 15, and S = B/9, giving B = 13.5 km/hr. The claimed answer B is correct.

Multiple choice
  1. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

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

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

  4. Quantity I < Quantity II मात्रा I < मात्रा II

  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
C Correct answer
Explanation

Quantity I: Downstream speed = 45/5 = 9 km/h, Upstream speed = 60/15 = 4 km/h. Boat speed = (9+4)/2 = 6.5 km/h. Quantity II: Downstream speed = 56/7 = 8 km/h, Stream speed = 2.5 km/h. Boat speed = 8 - 2.5 = 5.5 km/h. Therefore Quantity I (6.5) > Quantity II (5.5).

Multiple choice

Two boats in two parallel canals started at the same time in the same direction from the same place. One is travelling upstream and the other is travelling downstream. If both the boats reach the finish line at the same time, the boat speed in still water of upstream travelling 'x' and the speed boat in still water of downstream travelling boat 'y' if the speed of the stream in both canals is 10 km/hr and the sum of their speeds is 40km/hr. The possible value of x and y दो समानांतर नहरों में दो नाव उसी स्थान से उसी दिशा में एक ही समय में चलना प्रारंभ किया एक उर्ध्वप्रवाह जा रही है और दूसरी अनुप्रवाह , दोनों नावे एक साथ फिनिस बिंदु पर पहुचती हैं, उर्घ्व प्रवाह चलने वाली नाव की शांत जल में चाल 'x' और अनुप्रवाह चलने वाली नाव की शांत जल में चाल 'y' है, यदि दोनों नहरों में धारा की गति 10 किमी/घंटा है और नावों की गति का योग 40 किमी/घंटा है तो. x और y का संभावित मान है- a) 30 , 20 b) 30, 10 c) 20 ,10 d) 10 , 20

  1. Only a केवल a

  2. Both a, and b a, तथा b दोनों

  3. All a, b and C a, b तथा C

  4. Only b केवल b

  5. All a, b, c, and d a, b, c, तथा d सभी

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speed of stream be 10 km/hr. Upstream effective speed = x-10, downstream = y+10. They reach same time, so distances are same. Let distance = D. Time for upstream = D/(x-10), downstream = D/(y+10). These are equal, so D/(x-10) = D/(y+10), giving x-10 = y+10, or x-y = 20. Also x+y = 40 (given). Solving: x = 30, y = 10. Checking options: (30, 20) - no; (30, 10) - yes; (20, 10) - no; (10, 20) - no. The claimed answer (b: 30, 10) is correct.

Multiple choice
  1. 4 kmph, 9 kmph

  2. 8 kmph, 5 kmph

  3. 9 kmph, 4 kmph

  4. 5 kmph, 8 kmph

  5. 10 kmph, 3 kmph

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = b, stream speed = s. Upstream = b-s, downstream = b+s. 65/(b-s) + 130/(b+s) = 23 and 45/(b-s) + 104/(b+s) = 17. Solving: b+s = 13, b-s = 5. Therefore b = 9 kmph, s = 4 kmph.