Boats and Streams problems
- 1. Mahesh rows to the place 80 km away and back in 20 hours. He finds that he can row 8 km downstream in the same time as 4 km upstream. The speed of the boat in stillwater is
Options- A. 9 kmph
- B. 7 kmph
- C. 2 kmph
- D. 5 kmph Discuss
Correct Answer: 9 kmph
Explanation:
Downstream speed = 8/X kmph
upstream speed = 4/X kmph
Now 80/(8/X) + 80/(4/X)=20
X=2/3
downstream Speed = 8/(2/3)= 12 kmph
upstream Speed = 4/(2/3)= 6 kmph
Rate of the stream = (12+6)/2= 9 kmph
- 2. Equal distance is covered by a boat in upstream and in downstream in total 5 hours. Sum of speed of a boat in upstream and downstream is 40 km/hr. Speed of boat in still water is 600% more than the speed of stream. Find theapproximate distance covered by boat in downstream (in km).
Options- A. 45
- B. 50
- C. 55
- D. 60 Discuss
Correct Answer: 50
Explanation:
let speed of boat= X, speed of stream= Y
Upstream speed= X-Y
Downstream speed= X+Y
Sum of upstream & downstream= (X-Y) +(X+Y)= 2X
So, 2X= 40
X= 20 km/hr
Speed of boat : speed of stream= 600+100 :100= 7:1
So speed of Stream= 20/7 km/hr
ATQ, D/( X-Y) + D/( X+Y) = 5
D/(120/7) + D/(160/7)= 5
D= 480×5/49= 48.97 km= 50 Km(approx)
- 3. A boat takes 2 hours to travel from point A to B in still water. To find out its speed upstream, which of the following information is/are required? A. Distance between point A and B. B. Time taken to travel downstream from B to A. C. Speed of the stream of water.
Options- A. Only A and B
- B. Only B and C
- C. All are required
- D. Any one pair of A and B, B and C or C and A is sufficient Discuss
Correct Answer: Any one pair of A and B, B and C or C and A is sufficient
Explanation:
Let distance between A & B = d km
Let speed in still water = x kmph
Let speed of current = y kmph
from the given data,
d/x = 2
From A) we get d
From B) we get d/x+y
From C) we get y
So, Any one pair of A and B, B and C or C and A is sufficient to give the answer i.e, the speed of upstream.
- 4. Choose the most appropriate answer: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 9 Km/h and the speed of the current is 3 Km/h, the distance between A and B is
Options- A. 9 km
- B. 10 km
- C. 11 km
- D. 12 km Discuss
Correct Answer: 12 km
Explanation:
Speed of boat in still water = 9 km/hr
Speed of current = 3km/hr
Downstream speed = 9+3 = 12 km/hr
Upstream speed = 9-3 =6 km/hr
Let the distance between A to B be x km.
x/6 + x/12 = 3x + 2x = 36
3x = 36
x = 12 km
- 5. If a boat goes a certain distance at 30 km/hr and comes back the same distance at 60 km/hr. What is the average speed (in km/hr) for the total journey?
Options- A. 45
- B. 50
- C. 40
- D. 35 Discuss
Correct Answer: 40
- 6. A steamer moves with a speed of 4.5 km/h in still water to a certain upstream point and comes back to the starting point in a river which flows at 1.5 km/h. The average speed of steamer for the total journey is
Options- A. 12 km/h
- B. 10 km/h
- C. 6 km/h
- D. 4 km/h Discuss
Correct Answer: 4 km/h
Explanation:
Speed of streamer = 4.5 km/hrSpeed of water = 1.5 km/hr
Downstream speed = 4.5+1.5 = 6 km/hr
Upstream speed = 4.5 -1.5 = 3 km/hr
Average Speed = (6 X 3) / 4.5 = 4km/hr
- 7. A boat goes a certain distance at 40 km/hr and comes back the same distance at 24 km/hr. What is the average speed (in km/hr) for the total journey?
Options- A. 32
- B. 28
- C. 34
- D. 30 Discuss
Correct Answer: 30
- 8. Speeds of a boat along the current and against the current are 14 km/hr and 7 km/hr respectively. What is the speed of boat (in km/hr) in still water?
Options- A. 3.5
- B. 7.5
- C. 10.5
- D. 9.5 Discuss
Correct Answer: 10.5
- 9. The ratio of the speed of a boat downstream and speed of the stream is 9:1. If the speed of the current is 3 km per hr, find the distance travelled by the boat upstream in 5 hours.
Options- A. 100 km
- B. 98 km
- C. 109 km
- D. 105 km Discuss
Correct Answer: 105 km
Explanation:
Let the speed of boat in still water is ?x? km/hr & that of stream is ?y? km/hr.
Then, ATQ
(x+y)/y = 9/1 9y = x + y
x = 8y
y = 3 km/hr
So, x = 24 km/hr
Upstream speed = 24-3 = 21 km/hr
Hence, distance travelled upstream in 5 hours = 21*5 = 105 km.
- 10. Ashok can row upstream at 8 kmph and downstream at 12kmph.What is the speed of the stream ?
Options- A. 6 km/hr
- B. 3 km/hr
- C. 2 km/hr
- D. 4.5 km/hr Discuss
Correct Answer: 2 km/hr
Explanation:
If the speed downstream is a kmph and the speedup stream is b kmph then
Speed of the stream = 1/2 x (a?b) kmph
Speed downstream a = 12kmph
Speed upstream b = 8 kmph
Speed of the stream = 1/2 x (a?b) = 1/2 x (12?8)= 4/2 = 2 kmph
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