Boats and Streams problems
- 1. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Options- A. 16 hours
- B. 18 hours
- C. 20 hours
- D. 24 hours Discuss
Correct Answer: 24 hours
Explanation:
Speed downstream = 10.5 kmph.
| ∴ Total time taken = | ❨ | 105 | + | 105 | ❩hours = 24 hours. |
| 7.5 | 10.5 |
- 2. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options- A. 3 km/hr
- B. 5 km/hr
- C. 8 km/hr
- D. 9 km/hr Discuss
Correct Answer: 8 km/hr
Explanation:
| Speed in still water = | 1 | (11 + 5) kmph = 8 kmph. |
| 2 |
- 3. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
Options- A. 2 : 1
- B. 3 : 1
- C. 3 : 2
- D. 4 : 3 Discuss
Correct Answer: 3 : 1
Explanation:
Then, his rate downstream = 2x kmph.
| ∴ (Speed in still water) : (Speed of stream) = | ❨ | 2x + x | ❩ | : | ❨ | 2x - x | ❩ |
| 2 | 2 |
| = | 3x | : | x |
| 2 | 2 |
= 3 : 1.
- 4. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Options- A. 2 : 1
- B. 3 : 2
- C. 8 : 3
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 8 : 3
Explanation:
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
| ⟹ | ❨ | x x 8 | 4 | ❩ | = (y x 4) |
| 5 |
| ⟹ | 44 | x =4y |
| 5 |
| ⟹ y = | 11 | x. |
| 5 |
| ∴ Required ratio = | ❨ | y + x | ❩ | : | ❨ | y - x | ❩ |
| 2 | 2 |
| = | ❨ | 16x | x | 1 | ❩ | : | ❨ | 6x | x | 1 | ❩ |
| 5 | 2 | 5 | 2 |
| = | 8 | : | 3 |
| 5 | 5 |
= 8 : 3.
- 5. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
Options- A. 2 hours
- B. 3 hours
- C. 4 hours
- D. 5 hours Discuss
Correct Answer: 4 hours
Explanation:
| Time taken to travel 68 km downstream = | ❨ | 68 | ❩hrs = 4 hrs. |
| 17 |
- 6. The speed of boat upstream and speed of boat downstream are 7 km/h and 13 km/h, respectively. Then the speed of stream and the speed of boat in still water is?
Options- A. 10 km/h and 3 km/h
- B. 15 km/h and 9 km/h
- C. 20 km/h and 6 km/h
- D. 40 km/h and 12 km/h Discuss
Correct Answer: 10 km/h and 3 km/h
Explanation:
Rate in still water=[(1/2)(u+v)] km/h
Rate of current=[(1/2)(u-v)] km/h
where u= speed of boat in downstream
v=speed of boat in upstream
Speed of boat in still water=[(1/2)(7+13)] =10 km/h
Speed of the stream =[(1/2)(13-7)]=3 km/h
- 7. The speed of a boat in still water is 10 km/h. If it can travel 26 km downstream and 14 km upstream in the same time , then the speed of stream is?
Options- A. 2 km/h
- B. 2.5 km/h
- C. 3 km/h
- D. None of these Discuss
Correct Answer: 3 km/h
Explanation:
Let the speed of the stream = x km/h
?Speed of boat in still water = 10 km/h
Speed of boat downstream = ( x + 10) km/h
Speed of boat upstream=(10 - x) km/h
? Time taken to travel 26 km downstream=[ 26 / ( 10 + x ) ] h
Time taken to travel 14 km upstream=[ 14 /( 10 - x )] h
? By condition [ 26 / ( 10 + x)]=[ 14 / ( 10 - x)]
? 26(10-x)=14(10+x)
? 260-26x =140 + 14x
? 40x=120
? x = 3 Here, speed of stream = 3 km/h
- 8. A boat goes 40 km. upstream in 8 hours and 36 km. downstream in 6 hours. The speed of the boat in standing water is?
Options- A. 6.5 km.hr
- B. 6 km/hr
- C. 5.5 km/hr
- D. 5 km/hr Discuss
Correct Answer: 5.5 km/hr
Explanation:
Speed upstream = (40/8) km/hr = 5 km/hr
Speed downstream = (36/6) km/hr = 6 km/hr
Speed of boat in still water = (5 + 6)/2 km/hr = 5.5 km/hr.
- 9. If a man's rate with the current is 12 km/hr and the rate of the current is 1.5 km/hr then man's rate against the current is?
Options- A. 9 km/hr
- B. 6.75 km/hr
- C. 5.25 km/hr
- D. 7.5 km/hr Discuss
Correct Answer: 9 km/hr
Explanation:
Let the rate against the current be x km/hr.
Then, (12 - x) / 2 = 1.5
? 12 - x = 3
? x = 9 km/hr
- 10. If a man rows at 5 km/hr in still water and 3.5 km/hr against the current his rate along the current is?
Options- A. 8.5 km/hr
- B. 6.5 km/hr
- C. 6 km/hr
- D. 4.25 km/hr Discuss
Correct Answer: 6.5 km/hr
Explanation:
Speed of current = 5 - 3.5 = 1.5 km/hr.
So the speed of man along the current = 5 + 1.5 = 6.5 km/hr
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