Boats and Streams problems
- 1. 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
- 2. 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.
- 3. 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.
- 4. 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.
- 5. 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.
- 6. 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
- 7. 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.
- 8. 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.
- 9. A person can row 8 1/2 km an hour in still water and he finds that it takes him twice as long to row up as to row down the river. The speed of the stream ?
Options- A. 1.78 kmph
- B. 2.35 kmph
- C. 2.83 kmph
- D. 3.15 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 2.83 kmph
Explanation:
Given speed of the person = 8 1/2 = 17/2 kmph
Let the speed of the stream = x kmph
speed of upstream = 17/2 - x
speed of downstream = 17/2 + x
But given that,
2(17/2 - x) = 17/2 + x
=> 3x = 17/2
=> x = 2.83 kmph.
- 10. Amith can row a boat d km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat 2d km upstream in 7 hours. How long will it take to row the same distance 2d km downstream for Amith ?
Options- A. 4 hrs 10 min
- B. 3 hrs 15 min
- C. 3 hrs 30 min
- D. 4 hrs 1 min Also asked in: GATE, Bank Clerk, Bank PO, AIEEE, Bank Exams, CAT
Correct Answer: 3 hrs 30 min
Explanation:
Let the speed of boat and stream be x and y kmph respectively.
According to question
d/x+y + d/x-y = 5h 15m or 21/4 hrs ......(i)
and 2d/x-y = 7...... (ii)
From eq. (i) and (ii)
2d/x+y = 7/2
Hence, Amith will take to row 2d km distance downstream in 7/2 hrs
= 3.5 hrs
= 3 hrs 30 min.
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