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- Question
- A man can row against the current three-fourth of a kilometre in 15 min and returns same distance in 10 min, then ratio of his speed to that of current is?
Options- A. 3 : 5
- B. 5 : 3
- C. 1 : 5
- D. 5 : 1
- Correct Answer
- 5 : 1
ExplanationLet the speed of man and current be U and V km/h, respectively.
Speed upstream = (U - V) km/h
Speed down stream = (U + V) km/h
According to the question,
(3 x 60)/(4 x 15) = U - V
? U - V = 3 ......(i)
and (3/4) x (60/10) = U + V
? U + V = 9/2 ...(ii)
On adding Eqs. (i) and (ii), we get
2U = 3 + 9/2
? U = 15/4
On putting the value of U in Eq. (ii), we get
15/4 + V = 9/2
V = 9/2 - 15/4 = 18 - 15/4
? V = 3/4
Hence, speed of man U = 15/4 and
Speed of current V = 3/4
Hence, required ratio = 15/4 : 3/4 = 5 : 1 - 1. In a river, the ratio of the speed of stream and speed of a boat in still water is 2 : 5 Again, ratio of the speed of stream and speed of an another boat in still water is 3 : 4. What is the ratio of the speeds of the first boat to the second boat in still water?
Options- A. 10 : 7
- B. 15 : 8
- C. 4 : 3
- D. 5 : 4 Discuss
- 2. A steamer goes downstream from one port to another in 4 h. It covers the same distance upstream in 5 h. If the speed of the stream is 2 km/h, then find the distance between the two ports.?
Options- A. 50 km
- B. 60 km
- C. 70 km
- D. 80 km Discuss
- 3. A boat running upstream covers a distance of 10 km in 30 min and while running downstream, it covers the same distance in 25 min away and return, then the speed of the water current is?
Options- A. 2 km/h
- B. 3 km/h
- C. 1/2 km/h
- D. 1 km/h Discuss
- 4. A boat takes 9 h to travel a distance upstream and taken 3 h to travel the same distance downstream. If the speed of the boat in still water is 4 km/h, then what is the velocity of the stream?
Options- A. 4 km/h
- B. 3 km/h
- C. 6 km/h
- D. 2 km/h Discuss
- 5. A boat's speed in still water is 5km/h. While river is flowing with a speed of 2km/h and time taken to cover a certain distance upstream is 2 h more than time taken to cover the same distance downstream. Find the distance?
Options- A. 10.5 km
- B. 11 km
- C. 10.9 km
- D. 15 km Discuss
- 6. A boat running upstream takes 528 min to cover a certain distance, while it takes 240 min to cover the same distance running downstream. What is the ratio between the speed of the water current, respectively?
Options- A. 2 : 1
- B. 3 : 2
- C. 8 : 3
- D. Couldn't be determined Discuss
- 7. A motorboat travelling at the same speed, can cover 25 km upstream and 39 km downstream in 8 h. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 h. The speed of the stream is?
Options- A. 2 km/h
- B. 3 km/h
- C. 4 km/h
- D. 5 km/h Discuss
- 8. The speed of a boat in still water is 4 km/hr and the speed of current is 2 km/hr. If the time taken to reach a certain distance upstream is 9 hours, find the time it will take to go same distance downstream?
Options- A. 2 hrs
- B. 2.5 hrs
- C. 3.5 hrs
- D. 3 hrs Discuss
- 9. Ramesh can row a certain distance downstream is 6 hours and return the same distance in 9 hours. If the speed of Ram, Ramesh in still water is 12 km/hr, find the speed of the stream.
Options- A. 2.4 km/hr
- B. 2 km/hr
- C. 3 km/hr
- D. Data inadequate Discuss
- 10. A man rows to a place 48 km distance and back in 14 hours . He finds that he can row 4 km with the stream in the same time as 3 km against the stream. Find the rate of the stream?
Options- A. 1 km/hr
- B. 2 km/hr
- C. 1.5 km/hr
- D. 2.5 km/hr Discuss
Boats and Streams problems
Search Results
Correct Answer: 15 : 8
Explanation:
For the first boat,
Speed of stream : Speed of boat = 2: 5
Let speed of stream be 2x km/h and speed of boat = 5x km/h
Similarly, for the second boat
Speed of stream be 3y km/h and speed of boat = 4y
In both of the conditions, river is same.
? 2x = 3y
? x = 3y/2
Thus, required ratio in speeds of boats in still water
= Thus, required ratio in speeds of boats in still water
= 5x : 4y = (5 x 3)y/2 : 4y = 15 : 8
Correct Answer: 80 km
Explanation:
Let the distance between the two ports be x km.
Then, speed downstream = x/4
And speed upstream = x/5
? Speed of the stream = [speed downstream + speed upstream] / 2 = (x/4 - x/5)/2
? (5x -4x)/40 = 2
? x/40 = 2
? x = 80 km
Correct Answer: 1/2 km/h
Explanation:
Speed upstream = 10 / (30/60) = (10 x 60)/30 = 20 km/h
Speed downstream = 10/(25/60) = (10 x 60)/25 = 24 km/h
? Speed of the river's current = (24 - 20)/2 = 4/2 = 2 km/h
Correct Answer: 2 km/h
Explanation:
Let velocity of the stream be x km/h
? Velocity of the boat downstream = (4 + x) km/h
and velocity of the boat upstream = (4 - x) km/h
According to the question, 3(4 + x) = 9(4 - x)
? 12 + 3x = 36 - 9x
? 12x = 24
? x = 2 km/h
Correct Answer: 10.5 km
Explanation:
Let the distance be D km.
Speed download = (5 +2) = 7 km/h
and speed upstream = (5 -2) = 3 km/h
According to the question,
D/3 - D/7 = 2
? 7D - 3D = 21 x 2
? D = (21 x 2)/4 = 10.5 km
Correct Answer: 8 : 3
Explanation:
Let boat's rate upstream be U and boat's rate downstream = V
According to the question.
Distance covered in 528 min = Distance covered in 240 min
? Distance covered in 8 h 48 min = Distance covered in 4 h
? U x 84/5 = V x 4
? (44 x U)/5 = 4V
? V = (11 x U)/5
? Required ratio = (V + U)/2 : (V - U)/2
? = (11U/5 + U)/2 : (11U/5 - U)/ 2
? = 16U/5 : 6U/5 = 8 : 3
Correct Answer: 4 km/h
Explanation:
Let the speed of a boat and stream be U and V km/h
? Speed of boat along stream = (U + V) km/h
and speed of boat against stream = (U - V) km/h
According to the question,
25/(U - V) + 39/(U + V) = 8 ....(i)
and 35/(U - V) + 52/(U + V ) = 11 ..(ii)
On multiplying Eq. (i) by 4 and Eq. (ii) by 3, then subtract Eq. (ii) from Eq, we get
100/(U - V) - 105/(U - V) = -1
? 5/(U - V) = 1
? U - V = 5 ...(iii)
On substituting the value of (U - V) = 5 in Eq. (i) we get
25/5 + 39/(U + V) = 8
? 39/(U + V) = 8 - 5
? U + V = 39/3
? U + V = 13 ....(iv)
On solving Eqs. (iii) and (iv), we get
U = 9 and V = 4
Hence, speed of stream = 4 km/h
Correct Answer: 3 hrs
Explanation:
Upstream distance = (4 - 2) x 9 = 18 km
? Required time = 18/(4 + 2) = 3 hrs.
Correct Answer: 2.4 km/hr
Explanation:
? [(9 + 6)/(9 - 6)] x v = 12
? v = 2.4 km/hr
Correct Answer: 1 km/hr
Explanation:
Suppose that the man takes H hours to cover 4 km downstream and H house to cover 3 km upstream.
Then, 48H/4 + 48H/3 = 14
? H = 1/2
? Rate upstream = 3/(1/2)= 6 km/hr
and rate downstream = 4/(1/2) = 8 km/hr
? Rate of the stream = (8 - 6)/2 = 1 km/hr .
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