56488.Ratio between speed of boat in still water to speed of stream is 5 : 2. If 224 km is travelled by downstream in 4 hours then find the difference between speed of boat in still water and speed of stream?
24 km/hr
22 km/hr
28 km/hr
24 km/hr
Explanation:
Let the speed of boat in still water and speed of stream be 5x and 2x respectively.
According to the question,
$\dfrac{224}{4}=5x+2x$
x=$\dfrac{224}{7} \times 4 $
x=$\dfrac{32}{4}=8$
Required difference =5x-2x=3x
3x=24 km/hr
Let the speed of boat in still water and speed of stream be 5x and 2x respectively.
According to the question,
$\dfrac{224}{4}=5x+2x$
x=$\dfrac{224}{7} \times 4 $
x=$\dfrac{32}{4}=8$
Required difference =5x-2x=3x
3x=24 km/hr
56489.In a river, the ratio of the speed of the stream and the speed of a boat in still water is 5 : 7. Again, the ratio of the speed of the stream to the speed of another boat in still water is 6 : 8. What is the ratio of the speed of the first boat to that of the second boat in still water?
27 : 29
21 : 20
27 : 28
19 : 17
Explanation:
For the first boat let the speed of the stream be 5x and the speed of the boat be 7x.
For the 2nd boat, let the speed of the stream be 6y and the speed of the 2nd boat be 8y.
The speed of the stream will be the same.
∴ 5x = 6y
or x=6/5 y
Now, the required ratio of the speed of the first boat to that of the second boat = 7x : 8y
7*6/5y : 8y
[Putting x in terms of y]
y:
For the first boat let the speed of the stream be 5x and the speed of the boat be 7x.
For the 2nd boat, let the speed of the stream be 6y and the speed of the 2nd boat be 8y.
The speed of the stream will be the same.
∴ 5x = 6y
or x=6/5 y
Now, the required ratio of the speed of the first boat to that of the second boat = 7x : 8y
7*6/5y : 8y
[Putting x in terms of y]
y:
56490.Two boats A and B start towards each other from two places, 150 km apart. Speed of the boat A and B in still water are 16 km/hr and 14 km/hr respectively. If A proceeds down and B up the stream, they will meet after.
4.5 hours
4 hours
5 hours
6 hours
Explanation:
Let the speed of the stream be x kmph and both the boats meet after t hours.
According to the question,
Distance covered while going downstream + Distance covered while going upstream = Total Distance
⇒ (16 + x) t + (14 – x) t = 150
⇒ 16t + 14t = 150
⇒ 30t = 150
⇒ t = 5 hrs
Let the speed of the stream be x kmph and both the boats meet after t hours.
According to the question,
Distance covered while going downstream + Distance covered while going upstream = Total Distance
⇒ (16 + x) t + (14 – x) t = 150
⇒ 16t + 14t = 150
⇒ 30t = 150
⇒ t = 5 hrs
56491.Amit goes Mumbai to Kolkata by sea route. The speed of the boat in still water is 60 km/h and speed of the current is 15 km/h. After reaching Kolkata he stayed there for 20 minutes and after that come back by same boat. The time taken by him in this journey is 19 hours 32 minutes, find the distance travel by him in one side.
450 km
360 km
540 km
600 km
Explanation:
Time taken by him in travelling = 19 hours 32 minutes – 20 minutes
= 19 hours 12 minutes
Let Distance = x km
According to the question,
$\dfrac{x}{60 +15}+ \dfrac{x}{60-15}=19\dfrac{12}{60}$
$\dfrac{x}{75}+\dfrac{x}{45}=\dfrac{96}{5}$
$\dfrac{5x+3x}{225}=\dfrac{96}{5}$
$\dfrac{8x}{225}=\dfrac{96}{5}$
x=540 km
Time taken by him in travelling = 19 hours 32 minutes – 20 minutes
= 19 hours 12 minutes
Let Distance = x km
According to the question,
$\dfrac{x}{60 +15}+ \dfrac{x}{60-15}=19\dfrac{12}{60}$
$\dfrac{x}{75}+\dfrac{x}{45}=\dfrac{96}{5}$
$\dfrac{5x+3x}{225}=\dfrac{96}{5}$
$\dfrac{8x}{225}=\dfrac{96}{5}$
x=540 km
56492.Distance between a point of A and point B in a river is 12 km and the flow of the stream is from A to B. If the speed of the boat is 4 km/h and speed of the stream is 2 km/h. The boat goes from B to A and then comes back. What is the distance between point A and the boat after 7 hours of travel since the time of starting?
2 km
3 km
4 km
6 km
Explanation:
The resulting speed in upstream is 4 – 2= 2 km/h.
And the resulting speed in downstream is 4 + 2= 6 km/h.
Since the boat is moving upstream from B to A.
So time taken is 12/2 =6 hours.
Now in downstream it takes 12/6 =2 hours
So in 1 hour it will travel half the distance = 6 km.
So the distance of the boat from point A after 7 hours of travel will be 6 km.
The resulting speed in upstream is 4 – 2= 2 km/h.
And the resulting speed in downstream is 4 + 2= 6 km/h.
Since the boat is moving upstream from B to A.
So time taken is 12/2 =6 hours.
Now in downstream it takes 12/6 =2 hours
So in 1 hour it will travel half the distance = 6 km.
So the distance of the boat from point A after 7 hours of travel will be 6 km.
56493.A steamer can go 12 km in still water in 25 minutes. One day, it went 11.25 km upstream and returned the same distance in downstream. If the difference between the time taken to travel upstream and downstream was 12.5 minutes, then what was the speed of stream in km per hour?
7.2
5.4
6.3
4.5
Explanation:
In still water, the speed of steamer =$\dfrac{12000}{25}$
=480 meter per minute=8 meters per second
Let the speed of stream=v m/sec
In upstream,the speed of streamer=(8-v)m/sec
In downstream,the speed of streamer=(8+v) m/sec
According to the question,
$\dfrac{11250}{8-v}-\dfrac{11250}{8+v}$=$12.5 \times 60 $=750 seconds.
By solving,v=2 meters per second
=$\dfrac{2 \times 18}{5}$=7.2km per hour
In still water, the speed of steamer =$\dfrac{12000}{25}$
=480 meter per minute=8 meters per second
Let the speed of stream=v m/sec
In upstream,the speed of streamer=(8-v)m/sec
In downstream,the speed of streamer=(8+v) m/sec
According to the question,
$\dfrac{11250}{8-v}-\dfrac{11250}{8+v}$=$12.5 \times 60 $=750 seconds.
By solving,v=2 meters per second
=$\dfrac{2 \times 18}{5}$=7.2km per hour
56494.A boat travels upstream from point A to B in 5 hours. What is the distance between A and B, if it takes 2.5 hours to travel downstream from point B to A and speed of stream is 1 km per hour?
8 km
12 km
10 km
20 km
Explanation:
Let the speed of Boat be x km/hr
So the speed while going upstream will be (x – 1) km/hr and the speed going downstream will be (x + 1) km/hr
Since the distance traveled is the same, the equation can be formed as:
(x – 1) × 5 = (x + 1) × 2.5
⇒ x = 3
The distance between A and B is (3 + 1) × 2.5 = 10 km
Let the speed of Boat be x km/hr
So the speed while going upstream will be (x – 1) km/hr and the speed going downstream will be (x + 1) km/hr
Since the distance traveled is the same, the equation can be formed as:
(x – 1) × 5 = (x + 1) × 2.5
⇒ x = 3
The distance between A and B is (3 + 1) × 2.5 = 10 km
56495.Meera covers 20 km upstream in 600 minutes and she also covers 60 km downstream in 5 hours. Then find the rate of current of the river.
2.5 km/h
8 km/h
3 km/h
5 km/h
Explanation:
Let speed of Boat = x km/h, Speed of stream = y km/h
upstream speed=Distance/Time
x-y=$\dfrac{20}{(600 / 60)}
x-y=2km/h ....(1)
Downstream speed=Distance/Time
x+y=60/5
x+y=12km/h ....(2)
Subtracting Equation (1) by Equation (2)
y = 5 km/h.
Let speed of Boat = x km/h, Speed of stream = y km/h
upstream speed=Distance/Time
x-y=$\dfrac{20}{(600 / 60)}
x-y=2km/h ....(1)
Downstream speed=Distance/Time
x+y=60/5
x+y=12km/h ....(2)
Subtracting Equation (1) by Equation (2)
y = 5 km/h.
56496.If the ratio of speed of boat in downstream and speed of stream is 9 : 1, speed of current is 3 km per hr, What would be the distance travelled in upstream by the boat in 5 hours?
90 km
97 km
115 km
105 km
Explanation:
Ratio of speed of boat in downstream and speed of stream is 9 : 1
Given Speed of current = 3 km/ h
Speed of boat in downstream = 9 × 3 = 27 km/h
Speed of boat in still water = Speed of boat in downstream – Speed of current
= 27 – 3 = 24 km/h
Speed of boat in upstream = 24 – 3 = 21 km/h
Distance travelled by boat in upstream in 5 hours = 21 × 5 = 105 km
Ratio of speed of boat in downstream and speed of stream is 9 : 1
Given Speed of current = 3 km/ h
Speed of boat in downstream = 9 × 3 = 27 km/h
Speed of boat in still water = Speed of boat in downstream – Speed of current
= 27 – 3 = 24 km/h
Speed of boat in upstream = 24 – 3 = 21 km/h
Distance travelled by boat in upstream in 5 hours = 21 × 5 = 105 km
56497.The speed of a boat along the stream is 8 km/h and against the stream is 6 km/hr. The time taken by the boat to sail 28 km in still water is
2 hrs
3 hrs
4 hrs
8 hrs
Explanation:
Given, Speed downstream = 8 km/h Speed upstream = 6 km/h
∴ Speed of boat in still water= speed downstream +speed upstream /2.
=$\dfrac{8+6}{2}$
=$\dfrac{14}{2}$
=7 km/hr
Required time =Distance/speed of boat = 28/7 =4hrs.
Given, Speed downstream = 8 km/h Speed upstream = 6 km/h
∴ Speed of boat in still water= speed downstream +speed upstream /2.
=$\dfrac{8+6}{2}$
=$\dfrac{14}{2}$
=7 km/hr
Required time =Distance/speed of boat = 28/7 =4hrs.
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