Boats and Streams problems
- 1. A man 8 km/hr in still water. If the river is running at 2 km/hr, it taken 32 minutes to row to a place and back. How for is the place?
Options- A. 1.5 km
- B. 2.5 km
- C. 2 km
- D. 3 km Discuss
Correct Answer: 2 km
Explanation:
? D/(8 - 2) + D/(8 + 2) = 32/60
? D/6 + D/10 = 32/60
? 10D + 6D = 32
? D = 2 km
- 2. A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in 6 1/ 2 hours. The velocity of the current is?
Options- A. 1.5 km/hr
- B. 1 km/hr
- C. 2 km/hr
- D. 2.5 km/hr Discuss
Correct Answer: 2 km/hr
Explanation:
Let the speed upstream be U km/hr and the speed downstream be V km/hr respectively.
Then 24/U + 36/V = 6 ...(i)
and 36/U + 24/V = 13/2 ...(ii)
Solving these 2 equations we get
? U = 8 km/hr and V = 12 km/hr
? Velocity of current = (12 - 8)/2 km/hr = 2 km/hr
- 3. A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9km/hr and the speed of the current is 3 km/hr the distance between A and B is?
Options- A. 4 km
- B. 6 km
- C. 8 km
- D. 12 km Discuss
Correct Answer: 12 km
Explanation:
Speed downstream = (9 + 3) km/hr = 12km/hr
Speed upstream = = (9 - 3) km/hr = 6km/hr
Let the distance AB = d km
Then, d/6 + d/12 = 3
? 2d + d = 36
? d = 12
? Distance AB = 12 km
- 4. A man can swim 3 km/hr in still water. If the velocity of the stream be 2 km/hr, the time taken by him to swim to a place 10 km upstream and back is?
Options- A. 81/3 hrs
- B. 91/5 hrs
- C. 10 hrs
- D. 12 hrs Discuss
Correct Answer: 12 hrs
Explanation:
Speed upstream = (3 - 2) km/hr = 1 km/hr
Speed downstream = (3 + 2) km/hr = 5 km/hr
Total time taken = (10/1 + 10/5) hr = 12 hrs.
- 5. A man can row three quarters of a kilometre against the stream in 11 1/ 4 minutes and return in 7 1/ 2 minutes. The speed of the man in still water is?
Options- A. 2 km/hr
- B. 3 km/hr
- C. 4 km/hr
- D. 5 km/hr Discuss
Correct Answer: 5 km/hr
Explanation:
Speed upstream = (3/4) x (4/45 x 60 km/hr = 4 km/hr
Speed upstream = (3/4) x (2/15) x 60 km/hr = 6 km/hr
? Speed in still water = (4 + 6)/2 km/hr = 5 km/hr
- 6. A man can row 9 1/ 3 in still water and he finds that it takes him thrice as much time to row up than as to row down the same distance in river. The speed of the current is?
Options- A. 31 / 3 km/hr
- B. 31/3 km/hr
- C. 11/4 km/hr
- D. 42/3 km/hr Discuss
Correct Answer: 42/3 km/hr
Explanation:
Let speed upstream = x km/hr
Then, speed downstream = 3x km/hr
? Speed in still water = (x + 3x)/2 km/hr = 2x km/hr
Speed of the current = (3x - x)/2 km/hr = x km/hr
&becaus 2x = 28/3
? x = 14/3 = 42/3 km/hr.
- 7. The current of a stream runs at 1 km/hr. A motor boat goes 35 km upstream and back again to the starting point in 12 hours. The speed of motor boat in still water is?
Options- A. 6 km/hr
- B. 7 km/hr
- C. 8.5 km.hr
- D. 8 km/hr Discuss
Correct Answer: 6 km/hr
Explanation:
Let the speed in still water be x km/hr
? 35/(x - 1) + 35/(x + 1) = 12
? 35(2x) = 12(x2 - 1)
? 12x2 - 70x - 12 = 0
? 12x2 - 72x + 2x - 12 = 0
? 12x(x - 6) + 2 (x - 6) = 0
? (x - 6) (12x + 2) = 0
? x = 6 km/hr
- 8. A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is?
Options- A. 0.5 km/hr
- B. 1 km/hr
- C. 3.5 km/hr
- D. 1.8 km/hr Discuss
Correct Answer: 1 km/hr
Explanation:
Suppose he moves 4 km downstream in H hrs.
Then, Speed downstream = 4/H km/hr
Speed upstream = 3/H km/hr
T1 + T2 = 14
? (48 x H)/4 + (48 x H)/3 = 14
? 12H + 16H = 14
? H = 1/2
? Speed downstream = 8 km/hr
Speed upstream = 6 km/hr
? Rate stream = (8 - 6)/2 km/hr = 1 km/hr
- 9. Speed of a boat in standing water is 6 km/hr and the speed of the stream is 1.5 km/hr. A man rows to a place at a distance of 22.5 km and comes back to the starting point. The total time taken by him, is?
Options- A. 6 hrs 30 min
- B. 8 hrs 24 min
- C. 8 hrs
- D. 4 hrs 12 min Discuss
Correct Answer: 8 hrs
Explanation:
Speed upstream = (6 - 1.5) km/hr = 4.5 km/hr
Speed downstream = (6 + 1.5) km/hr = 7.5 km/hr
Total time taken = (22.5/4.5 + 22.5/7.5) hrs
= (5 + 3) hrs.
= 8 hrs.
- 10. A boat takes 3 hours to travel from place M to N downstream and back from N to M upstream. If the speed of the boat in still water is 4 km, what is the distance between the two places?
Options- A. 8 km
- B. 12 km
- C. 6 km
- D. Data inadequate Discuss
Correct Answer: Data inadequate
Explanation:
Let the distance between M and N and the speed of current be d km and x km/hr respectively.
According to the question = {d/(4 + x) + d/(4 - x)} = 3
In the above equation we have only one equations but two variables. Hence cannot be determined (Data inadequate).
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