Boats and Streams problems
- 1. A boat's man goes 48 km downstream in 8 hours and returns back in 12 hours. Find the speed of the boat in still water and the rate of the stream?
Options- A. 5 km/hr; 1 km/hr
- B. 10 km/hr; 2 km/hr
- C. 6 km/hr; 1.5 km/hr
- D. None of these Discuss
Correct Answer: 5 km/hr; 1 km/hr
Explanation:
Rate downstream = 48/8 = 6 km/hr
Rate upstream = 48/12 = 4 km/hr
? Speed of boat in still water = (6 + 4)/2 = 5 km/hr
Rate of stream = (6 -4)/2 = 1 km/hr
- 2. A man can row 60 km downstream in 6 hours. If the speed of the current is 3 km/hr, then find in what time will he be able to cover 16 km upstream?
Options- A. 4.5 hours
- B. 4 hours
- C. 5 hours
- D. 5.5 hours Discuss
Correct Answer: 4 hours
Explanation:
Downstream speed = 60/6 = 10 km/hr
Speed of stream = 3 km/hr
Upstream speed = 10 - (2 x 3) = 4 km/hr
? Required time = 16/4 = 4 hours.
- 3. speed of a boat in standing water is 7 km/hr and the speed of the stream is 1.5 km/hr. A distance of 7.7 km. going upstream is covered in?
Options- A. 1 hr. 15 min.
- B. 1 hr. 12 min.
- C. 1 hr. 24 min.
- D. 2 hr. 6 min. Discuss
Correct Answer: 1 hr. 24 min.
Explanation:
Upstream speed = 7 - 1.5 = 5.5 km/hr
? 5.5 x T = 7.7
? T = 77.7 / 5.5 = 1hr. 24 minutes
- 4. A sailor sails a distance of 48 km along the flow of a river in 8 h. If it takes 12 h to return the same distance, then the speed of the flow of the river is?
Options- A. 0.5 km/h
- B. 1 km/h
- C. 1.5 km/h
- D. 2 km/h Discuss
Correct Answer: 1 km/h
Explanation:
Let speed of the flow of water be x km/h and rate of sailing of sailor be y km/h.
Downstream speed (x + y) = 48/8
? x + y = 6 ....(i)
and upstream speed x - y = 4 ...(ii)
On solving Eqs. (i) and (ii), we get
y = 1 km/h
- 5. Sameer can row a certain distance downstream in 24 h and can come back covering the same distance in 36 h. If the stream flows at the rate of 12 km/h, find the speed of Sameer in still water?
Options- A. 30 km/h
- B. 15 km/h
- C. 40 km/h
- D. 60 km/h Discuss
Correct Answer: 60 km/h
Explanation:
Let the speed of Sameer in still water be x km/h
Sameer's speed downstream = (x + 12) km/h
Sameer's speed upstream = (x - 12) km/h
According to the question, 24(x + 12) = 36(x - 12)
? 2x + 24 = 3x - 36
? x = 36 + 24 = 60 km/h
- 6. Pawan can row 24 km/h in still water. When the river is running at 4.8 km/h, it takes him 1 h to row to a place and to come back. How far is the place?
Options- A. 11.52 km
- B. 14 km
- C. 12.52 km
- D. 15 km Discuss
Correct Answer: 11.52 km
Explanation:
Pawan's speed downstream = 24 + 4.8 = 28.8 km/h
Pawan's speed upstream = 24 - 4.8 = 19.2 km/h
Let the required distance be x.
According to the question.
x/28.8 + x/19.2 = 1
? (19.2x + 28.8x) / 552.96 = 1
? 19.2x + 28.8x = 552.96
? 48x = 552.96
? x = 552.96/48 = 11.52 km
- 7. A man can row 6 km/h in still water. If the speed of the current is 2 km/h, it takes 3 h more in upstream than in the downstream for the same distance. The distance is?
Options- A. 30 km
- B. 24 km
- C. 20 km
- D. 32 km Discuss
Correct Answer: 24 km
Explanation:
Let total distance be x km.
According to the question,
x/(6 + 2) + 3 = x/6 - 2
? x/8 + 3 = x/4
? x/4 - x/8 = 3
? 2x - x/8 = 3
? x = 8 x 3 = 24 km
- 8. The speed of the current is 5 km/h. A motorboat goes 10 km upstream and back again to the starting point in 50 min. The speed, (in km/h) of the motorboat in still water is?
Options- A. 20 km/h
- B. 26 km/h
- C. 25 km/h
- D. 28 km/h Discuss
Correct Answer: 25 km/h
Explanation:
Let speed of boat be x km/h.
Given speed of current = 5 km/h
? Upstream speed of boat = (x -5) km/h
Downstream speed of boat = (x + 5) km/h
According to the question.
10/(x - 5) + 10/(x + 5) = 50/60
? 10(x + 5 + x - 5)/( x2 - 25) = 5/6
? x2 -24x - 25 = 0
? x2 - 25x + x - 25 = 0
? (x - 25) (x + 1) = 0
? x = 25 [? x ? -1]
- 9. A boat cover a distance of 30 km downstream in 2 h while it takes 6 h to cover the same distance distance upstream. What is the speed of the boat (in km/h)?
Options- A. 5
- B. 7.5
- C. 13
- D. 10 Discuss
Correct Answer: 10
Explanation:
Speed of boat downstream = Distance covered / Time taken
= 30/2 = 15 km/h
Now, speed of boat upstream = Distance covered / Time taken
= 30/6 = 5 km/h
Now, speed of boat = (Speed download + Speed upstream) / 2
= (15 + 5) / 2 = 10 km/h
- 10. A man can row at 10 km/h in still water. If he takes total 5 h to go to a place 24 km away and return, then the speed of the water current is?
Options- A. 2 km/h
- B. 3 km/h
- C. 1/2 km/h
- D. 1 km/h Discuss
Correct Answer: 2 km/h
Explanation:
Let speed of water current be x km/h
? Speed downstream = (10 + x) km/h.
Speed upstream = (10 - x) km/h
According to the question,
24/(10 + x) + 24/(10 - x) = 5
? 24[10 - x + 10 + x] = 5(102 - x2)
? 100 - x2 = (24 x 20) / 5
? 100 - x2 = 96
? x2 = 4
? x = ?4 = 2km/h
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