Boats and Streams problems
- 1. Ashutosh can row 24 km/h in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream.?
Options- A. 4 km/h
- B. 18 km/h
- C. 8 km/h
- D. 15 km/h Discuss
Correct Answer: 8 km/h
Explanation:
Let rate of stream be 'a' km/h.
According to the question.
24 + a = 2(24 - a)
? 24 + a = 48 - 2a
? 3a = 48 - 24 = 24
? a = 24/3 = 8 km/h
- 2. A boat goes 12 km in 1 h in still water. It takes thrice time in covering the same distance against the current. Find the speed of the current.?
Options- A. 8 km/h
- B. 12 km/h
- C. 6 km/h
- D. 7 km/h Discuss
Correct Answer: 8 km/h
Explanation:
Speed of a boat in still water = distance / time = 12/1 = 12 km/h
Speed against the current = 12/3 km/h
Let the speed of the current = x km/h
According to the question,
12 - x = 4
? x = 8 km/h
- 3. A boatman takes twice as long to row a distance against the stream as to row the same distance with the stream. Find the ratio of speeds of the boat in still water and the stream.?
Options- A. 2 : 1
- B. 3 : 1
- C. 1 : 2
- D. 1 : 3 Discuss
Correct Answer: 3 : 1
Explanation:
Let boatman's speed upstream x
And his speed downstream = 2x
? Ratio = (Speed in still water) : (Speed of stream)
= (2x + x/2) : (2x - x/2)
= 3x/2 : x/2
= 3 : 1
- 4. A river is flowing with a steady speed of 4 km/h. One rows his boat downstream in the river and then returns by rowing upstream in the same river. When he returns to the starting points, the total distance covered by him is 42 km. If the return journey takes 2 h more than his outward journey, then the speed of his rowing in still water must be?
Options- A. 12 km/h
- B. 10 km/h
- C. 9 km/h
- D. 8 km/h Discuss
Correct Answer: 10 km/h
Explanation:
Let the speed of rowing in still water be u km/h.
Distance in downstream motion = 21 km
and speed downstream = (u + 4) km/h
? Time taken = 21/ (u + 4)
Distance upstream motion = 21 km and speed upstream = (u +4) km
? Time taken = 21/(u - 4)
According to the question.
21/(u + 4) + 2 = 21/(u - 4)
? (21 + 2u + 8)/u + 4 = 21/(u - 4)
? (2u + 29)/(u + 4) = 21/(u - 4)
? (u - 4) (2u + 29) = 21(u + 4)
? 2u2 - 8u + 29u - 116 = 21u + 84
? 2u2 + 21u - 116 = 21u + 84
? 2u2 = 84 + 116
? u2 = 200/2
? u2 = 100
? u = 10 km/h
- 5. A river is flowing at a speed of 5 km/h in a particular direction. A man, who can swim at a speed of 20 km/h in still water, starts swimming along the direction of flow of the river from from points A and reaches another point B which is at a distance of 30 km from the starting point A. On reaching point B, the man turns back and starts swimming against the direction of flow of the river and stops after reaching point A. The total time taken by the man to complete his journey is?
Options- A. 2 h 30 min
- B. 3 h 12 min
- C. 3 h 30 min
- D. 3 h 45 min Discuss
Correct Answer: 3 h 12 min
Explanation:
Given,
Speed of the stream = 5 km/h
and speed of the man in still water = 20 km/h
? Speed of the man downstream = 20 + 5 = 25 km/h
and speed of the man upstream = 20 - 5 = 15 km/h
? Total time taken to complete the whole journey = 30/25 + 30/15
= (30 x 8) / 75
= 3 h 12 min
- 6. Ishwar is rowing a boat. He takes half time in moving a certain distance downstream than upstream. What is the ratio of the rate of boat in still water to the rate of current?
Options- A. 2 : 1
- B. 5 : 1
- C. 7 : 1
- D. 3 : 1 Discuss
Correct Answer: 3 : 1
Explanation:
Let speed of Ishwar's boat in still water be x km/h
and speed of current = y km/h
Rate downstream = (x + y) km/h
Rate upstream = (x - y) km/h
Let the distance covered in each case be a.
According to the question,
2a/(x + y) = a/(x - y)
? 2(x - y) = x + y
2x - 2y = x + y
? x = 3y
? x/y = 3/1
? x : y = 3 : 1
- 7. A man can row 7 1/ 2 km/h in still water. If in a river running at 1.5 km/h, it takes him 50 min to row to a place and back, how far off is the place?
Options- A. 3 km
- B. 4 km
- C. 1 km
- D. 2 km Discuss
Correct Answer: 3 km
Explanation:
Let the distance be L km.
Speed of the main in still water = 71/2 km/h
and speed of the river = 15 km/h
? Speed of the man downstream = 7.5 + 1.5 = 9
Speed of the man upstream = 7.5 - 1.5 = 6 km/h
According to the question,
L/9 + L/6 = 50/60
? (4L + 6L)/36 = 50/60
? 10L/36 = 50/60
? L = (50 x 36)/(10 x 60)
5? x = 3 km
- 8. The ratio of speed of a motorboat to that of the current of water is 35 : 5. The motorboat goes along with the current in 5 h 10 min. Find the time to come back of motorboat?
Options- A. 5 h 50 min
- B. 6 h
- C. 6 h 50 min
- D. 12 h 10 min Discuss
Correct Answer: 6 h 50 min
Explanation:
Let speed of a motorboat be = 36k km/h
and speed of the current = 5k km/h
? Speed downstream = (36 + 5)k = 41k km/h
and speed upstream = (36 - 5)k = 31k km/h
Let distance be D km.
According to the question
When boat goes along with the current.
Distance = Time x Speed
? D = (5 + 10/60) x 41k
? D = 31/6 x 41k ....(i)
Again, when boat come back
a = Time x Speed
From Eq. (i) .
31/6 x 41k = Time x 31k
? Time = 41/6
Time = 6 h 50 min.
- 9. Ravi can row downstream at 9 km/h and upsteam at 5 km/h. Find the speed of Ravi in still water and speed of current.
Options- A. 7 km/h and 2 km/h
- B. 8 km/h and 6 km/h
- C. 7 km/h and 3 km/h
- D. 8 km/h and 2 km/h Discuss
Correct Answer: 7 km/h and 2 km/h
Explanation:
Given, downstream speed = 9 km/h
and upstream speed = 5 km/h
According to the formula
Ravi's speed in still water = (Speed downstream + Speed upstream )/2
= 1/2(9 + 5) = 14/2 = 7 km/h
and speed of current = (Speed downstream - Speed upstream)/2
= (9 - 5)/2 = 4/2 = 2 km/h.
- 10. A boatman row 1 km in 5 min along the steam and 6 km in 1 h against the stream. The speed of the steam is?
Options- A. 3 km/h
- B. 6 km/h
- C. 10 km/h
- D. 12 km/h Discuss
Correct Answer: 3 km/h
Explanation:
Let the speed of boat and steam be x and y km/h.
? Speed of boat along steam = (x + y) km/h
and speed of boat against stream = (x - y) km/h
According to the question,
x + y = 1 / (5/60) = 60/5
? x + y = 12 ...(i)
and y - x = 6 ...(ii)
On adding Eqs. (i) and (ii), we get
2x = 18
x = 18/2 = 9
On putting the value of x in Eq. (i), We get
9 + y = 12
y = 12 - 9 = 3
Hence, speed of boat = 9 km/h
and speed of steam = 3 km/h
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