Boats and Streams problems
- 1. A man can row 8 kmh in still water. If the river is running at 2 kmh, it takes 4 hrs more upstream than to go downstream for the same distance. Then the distance is given by
Options- A. 54 kms
- B. 32 kms
- C. 45 kms
- D. 60 kms Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 60 kms
Explanation:
Let the distance be d.
=> 2d = 120
=> d = 60 kms.
- 2. A motorboat can go 10 miles downstream on a river in 20 min. It takes 30 min for this boat to go back at the same 10 miles. Find the speed of the current ?
Options- A. 8 m/h
- B. 5 m/h
- C. 7 m/h
- D. 6 m/h Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 5 m/h
Explanation:
As the distance travelled is constant, the time taken is inversely proportional to speed.
Let 'u' be the speed of the current and 'v' be the speed of the boat.
Speed of the boat downstream = v + u & upstream = v - u
=> v+u/v-u = 30/20 => v/u = 5 => v = 5u
=> v + u = 6u = 10/20/60 miles/hr
=> 6u = 30 m/h
=> u = 5 m/h
- 3. In one hour, a boat goes 12 km/hr along the stream and 6 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options- A. 9
- B. 8
- C. 7
- D. 7.5 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 9
Explanation:
Speed in still water = Average of Speed in Upstream and speed in Downstream
= 1/2 (12 + 6) kmph = 9 kmph.
- 4. If sum of upstream and downstream speed of a boat is 82 kmph, and the boat travels 105 km. upstream in 3 hr, Find the time taken by boat to cover 126 km downstream.
Options- A. 2.8 hrs
- B. 2.7 hrs
- C. 2.6 hrs
- D. 2.5 hrs Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 2.7 hrs
Explanation:
Let Speed of boat in still water = b
Let Speed of still water = w
Then we know that,
Speed of Upstream = U = boat - water
Speed of Downstream = D = boat + water
Given, U + D = 82
b - w + b + w = 82
2b = 82
=> b = 41 kmph
From the given data,
41 - w = 105/3 = 35
w = 6 kmph
Now,
b + w = 126/t
=> 41 + 6 = 126/t
=> t = 126/47 = 2.68 hrs.
- 5. A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current ?
Options- A. 9 and 3 kmph
- B. 6 and 7 kmph
- C. 8 and 1 kmph
- D. 7 and 2 kmph Also asked in: AIEEE, Bank Exams, CAT, Bank PO
Correct Answer: 8 and 1 kmph
Explanation:
Downstream speed = 72km/8hrs = 9 kmph
upstream speed = 84km/12hrs = 7 kmph
speed of boat = avg of downstream and upstream speeds
speed of boat = (9+7)/2kmph = 8 kmph.
current speed = half of the difference of downstream and upstream speeds
currend speed = (9-7)/2kmph = 1 kmph
- 6. A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time he will be able to cover 8 km upstream ?
Options- A. 1.5 hrs
- B. 1 hrs
- C. 2.5 hrs
- D. 2 hrs Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 2 hrs
Explanation:
Speed in downstream = 96/8 = 12 kmph
Speed of current = 4 km/hr
Speed of the boatman in still water = 12 ? 4 = 8 kmph
Speed in upstream = 8 ? 4 = 4 kmph
Time taken to cover 8 km upstream = 8/4 = 2 hours.
- 7. Rajesh rows in still water with a speed of 4.5 kmph to go to a certain place and comes back. Find his average speed for the whole journey, if the river is flowing with a speed of 1.5 kmph?
Options- A. 2 kmph
- B. 4 kmph
- C. 6 kmph
- D. 8 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO, Database Administrator
Correct Answer: 4 kmph
Explanation:
Let the distance in one direction = k kms
Speed in still water = 4.5 kmph
Speed of river = 1.5
Hence, speed in upstream = 4.5 - 1.5 = 3 kmph
Speed in downstream = 4.5 + 1.5 = 6 kmph
Time taken by Rajesh to row upwards = k/3 hrs
Time taken by Rajesh to row downwards = k/6 hrs
Now, required Average speed =
Therefore, the average speed of the whole journey = 4kmph.
- 8. Find the speed of stream if a boat covers 36 km in downstream in 6 hours which is 3 hours less in covering the same distance in upstream?
Options- A. 1.5 kmph
- B. 1 kmph
- C. 0.75 kmph
- D. 0.5 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 1 kmph
Explanation:
Speed of the boat upstream = 36/9 = 4 kmph
Speed of the boat in downstream = 36/6 = 6 kmph
Speed of stream = 6-4/2 = 1 kmph
- 9. A man can row against the current three fourth of a kilometer in 15 min and returns same distance in 10 min, then ratio of his speed to that of current?
Options- A. 5:1
- B. 3:1
- C. 4:1
- D. 2:1 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, IT Trainer
Correct Answer: 5:1
Explanation:
Let the speed of the man in still water = p kmph
Speed of the current = s kmph
Now, according to the questions
(p + s) x 10 = (p - s) x 15
2p + 2s = 3p - 3s
=> p : s = 5 : 1
Hence, ratio of his speed to that of current = 5:1.
- 10. A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current ?
Options- A. 1 kmph
- B. 3.2 kmph
- C. 1.5 kmph
- D. 2 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 1.5 kmph
Explanation:
72 --- 9
? ---- 1
=> Down Stream = 8
45 ---- 9
? ---- 1
=> Up Stream = 5
Speed od current S = ?
S = (8 - 5)/2 = 1.5 kmph.
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