Aptitude - Boats and Streams - Discussion
Discussion Forum : Boats and Streams - General Questions (Q.No. 3)
3.
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Answer: Option
Explanation:
Let the man's rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
x x 8 | 4 | = (y x 4) | |||
5 |
44 | x =4y | |
5 |
y = | 11 | x. |
5 |
Required ratio = | y + x | : | y - x | ||||
2 | 2 |
= | 16x | x | 1 | : | 6x | x | 1 | ||||
5 | 2 | 5 | 2 |
= | 8 | : | 3 |
5 | 5 |
= 8 : 3.
Discussion:
107 comments Page 1 of 11.
Shivam said:
6 years ago
The speed of the boat in still water = Vb.
The speed of stream = Vs.
Question asked -- ratio, Vb : Vs = ?..
Vb + Vs = Vr1 (resultant speed downstream), and time taken to cover a distance "d" with speed Vr1 is 4 hrs.
Similarly,
Vb - Vs = Vr2 (resultant speed upstream), and time is taken to cover the same distance with speed Vr2 is 8 hrs, 48min.
By adding both the equations , we get
2Vb =Vr1 + Vr2.
Vb = (Vr1 + Vr2) 1/2.
lets find Vr1, which is distance d / time taken during upstream i.e Vr1 = d/4,
Similarly, Vr2 = d/(8 + 4/5),
= 5d/44.
in 60 min it is 1 hr so, in 1 min it is 1/60 hrs and in 48 min it is 1/60 * 48 = 4/5 hrs }
Putting Vr1 and Vr2 values in eq 3, we get -
Vb = 2d/11.
Putting value of Vb in eq 1 we'll get;
Vs = 3d/44.
Therefore, Vb/Vs = 8/3 Ans.
The speed of stream = Vs.
Question asked -- ratio, Vb : Vs = ?..
Vb + Vs = Vr1 (resultant speed downstream), and time taken to cover a distance "d" with speed Vr1 is 4 hrs.
Similarly,
Vb - Vs = Vr2 (resultant speed upstream), and time is taken to cover the same distance with speed Vr2 is 8 hrs, 48min.
By adding both the equations , we get
2Vb =Vr1 + Vr2.
Vb = (Vr1 + Vr2) 1/2.
lets find Vr1, which is distance d / time taken during upstream i.e Vr1 = d/4,
Similarly, Vr2 = d/(8 + 4/5),
= 5d/44.
in 60 min it is 1 hr so, in 1 min it is 1/60 hrs and in 48 min it is 1/60 * 48 = 4/5 hrs }
Putting Vr1 and Vr2 values in eq 3, we get -
Vb = 2d/11.
Putting value of Vb in eq 1 we'll get;
Vs = 3d/44.
Therefore, Vb/Vs = 8/3 Ans.
Amar The macho man said:
2 years ago
Given,
Time (upstream)=8 hour 48 min=(8*60+48) = 528 min.
Time (downstream)= 4 hour = (4*60)min = 240 min.
Let distance be x.
we know speed =distance/time.
so, the speed of the boat (upstream) = distance/time.
= x/528.
speed of the boat (downstream) = distance/time.
= x/240.
We know that;
speed of boat in still water = (downstream+upstream)/2.
= (x/240 + x/528)/2.
= x/330.
We know that
speed of stream/current water.
= (downstream-upstream)/2.
So we have to find the ratio of the speed of the boat in still water by the speed of the stream/current =
(x/330)/(x/528)=8/3 or 8:3
Therefore, ratio = 8:3 Answer.
Time (upstream)=8 hour 48 min=(8*60+48) = 528 min.
Time (downstream)= 4 hour = (4*60)min = 240 min.
Let distance be x.
we know speed =distance/time.
so, the speed of the boat (upstream) = distance/time.
= x/528.
speed of the boat (downstream) = distance/time.
= x/240.
We know that;
speed of boat in still water = (downstream+upstream)/2.
= (x/240 + x/528)/2.
= x/330.
We know that
speed of stream/current water.
= (downstream-upstream)/2.
So we have to find the ratio of the speed of the boat in still water by the speed of the stream/current =
(x/330)/(x/528)=8/3 or 8:3
Therefore, ratio = 8:3 Answer.
(51)
Saurabh gupta said:
8 years ago
Given explanation is quite difficult to understand. Let me explain you this in a simpler manner.
Distance is same during upstream and Downstream and Distance is equal to : Speed/Time.
So, time in downstream = 4 hours,
Time in upstream = 44/5 hours (8 hours 48mins).
Now let's assume x as the distance.
A as the downstream speed and B as the upstream speed.
Now write both (as the distance formula),
44/5 = x/B ---> equation 1.
4 = x/A ---> equation 2.
Solving these two equations we get,
44/20 = a/b ---> equation 3.
By equation 3, we can say that a = 44b/20
And we want to calculate u : v.
i.e 1/2(a + b) : 1/2(a - b),
i.e (a + b) : (a - b),
i.e 44b/20 + b : 44b/20 - b,
i.e 64b/20 : 24b/20,
i.e 64b : 24b,
i.e 8 : 3.
That's It. I know it's a bit lengthy But you would be able to calculate 3/4 of these steps orally.
Distance is same during upstream and Downstream and Distance is equal to : Speed/Time.
So, time in downstream = 4 hours,
Time in upstream = 44/5 hours (8 hours 48mins).
Now let's assume x as the distance.
A as the downstream speed and B as the upstream speed.
Now write both (as the distance formula),
44/5 = x/B ---> equation 1.
4 = x/A ---> equation 2.
Solving these two equations we get,
44/20 = a/b ---> equation 3.
By equation 3, we can say that a = 44b/20
And we want to calculate u : v.
i.e 1/2(a + b) : 1/2(a - b),
i.e (a + b) : (a - b),
i.e 44b/20 + b : 44b/20 - b,
i.e 64b/20 : 24b/20,
i.e 64b : 24b,
i.e 8 : 3.
That's It. I know it's a bit lengthy But you would be able to calculate 3/4 of these steps orally.
Debjani Nandy said:
9 years ago
Speed of the boat upstream = Speed of boat - Speed of stream.
Speed of stream = Speed of boat - Speed of the boat upstream--------- (1).
Speed of the boat downstream = Speed of boat + Speed of stream.
Speed of stream = Speed of the boat downstream - Speed of boat-------- (2).
Now, equating (1) & (2),
Speed of boat-speed of boat upstream = Speed of boat downstream - Speed of boat.
2 (Speed of boat) = Speed upstream + Speed downstream.
Speed of boat = (Speed upstream + Speed downstream)/2.
If, Speed upstream = x and Speed downstream = y then,
Speed of boat = (x+y)/2.
Similarly, making speed of the boat as subject in eq (1) & (2) and then equating we get,
Speed of stream = (Speed downstream - Speed upstream)/2.
= (y-x) /2.
Speed of stream = Speed of boat - Speed of the boat upstream--------- (1).
Speed of the boat downstream = Speed of boat + Speed of stream.
Speed of stream = Speed of the boat downstream - Speed of boat-------- (2).
Now, equating (1) & (2),
Speed of boat-speed of boat upstream = Speed of boat downstream - Speed of boat.
2 (Speed of boat) = Speed upstream + Speed downstream.
Speed of boat = (Speed upstream + Speed downstream)/2.
If, Speed upstream = x and Speed downstream = y then,
Speed of boat = (x+y)/2.
Similarly, making speed of the boat as subject in eq (1) & (2) and then equating we get,
Speed of stream = (Speed downstream - Speed upstream)/2.
= (y-x) /2.
Virendra kumar said:
4 years ago
Let,
Upstream speed = X kmph.
Downstream spead = Y kmph.
So,
We know that distance is the same.
And we know, D=SXT (speedxtime)
D= X(8+48/60) upstream case--->eq1
D=Y(4)---> eq 2
Now, equate both.
4Y = X(8+4/5).
4Y= X(44/5).
Y=X(11/5).
Y/X = 11/5.
So now relate as Y=11, X=5.
Now speed of water(S.W) = downstrean-upstream/2.
= Y-X/2.
=11-5/2 = 6/2 = 3.
Now, speed of boat = downstream - speed of the water.
= Y- (S.W).
= 11-3 = 8.
Now ratio of both as given in question,
Ratio of boat speed to water speed = 8/3.
Ratio = 8:3.
Hope you'll get it well.
Upstream speed = X kmph.
Downstream spead = Y kmph.
So,
We know that distance is the same.
And we know, D=SXT (speedxtime)
D= X(8+48/60) upstream case--->eq1
D=Y(4)---> eq 2
Now, equate both.
4Y = X(8+4/5).
4Y= X(44/5).
Y=X(11/5).
Y/X = 11/5.
So now relate as Y=11, X=5.
Now speed of water(S.W) = downstrean-upstream/2.
= Y-X/2.
=11-5/2 = 6/2 = 3.
Now, speed of boat = downstream - speed of the water.
= Y- (S.W).
= 11-3 = 8.
Now ratio of both as given in question,
Ratio of boat speed to water speed = 8/3.
Ratio = 8:3.
Hope you'll get it well.
(6)
Binza said:
1 decade ago
Speed=distance/time
therefore distance=speed*time.
let consider speed at upstream is "x" and at downstream is "y", then distance covered (upstream in 8 hrs 48 min)= x*8*4/5
here 8hours and 48minutes=8*48/60=8*4/5
and distance covererd (downstream in 4hours=y*4
to relate both these equation
from question ,we know that distance covered are same
therefore x*8*4/5 = y*4
y=11/(5*x)
we know that speed are different in down stream and upstream.
if both are in same direction
take difference(x-y)
if they are in opposite
take sum(x+y)
required ratio =(x+y)/2 : (x-y)/2 // here 2 is to take average.
then answer is 8:3
therefore distance=speed*time.
let consider speed at upstream is "x" and at downstream is "y", then distance covered (upstream in 8 hrs 48 min)= x*8*4/5
here 8hours and 48minutes=8*48/60=8*4/5
and distance covererd (downstream in 4hours=y*4
to relate both these equation
from question ,we know that distance covered are same
therefore x*8*4/5 = y*4
y=11/(5*x)
we know that speed are different in down stream and upstream.
if both are in same direction
take difference(x-y)
if they are in opposite
take sum(x+y)
required ratio =(x+y)/2 : (x-y)/2 // here 2 is to take average.
then answer is 8:3
Gautam said:
1 decade ago
Let the man's rate upstream be U kmph and that downstream be V kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
[U*8*48/60] = [V*4] [BECAUSE 1 MINUTE=60SECONDS]
[U*8*4/5] = [4V]
[U*44/5] = [4V]
44/5 U = 4V
THEN, USE THE FORMULA-----If the speed of the boat in still water is U km/hr and the stream of the boat is V km/hr then.
speed downstream = (u+v)km/hr
speed up stream = (u+v)km/hr
so, our U= 44/5 COME AND V= 4 COME
NOW, [U+V]/[U-V]
[44/5+4] / [44/5-4]
[44+20] / [44-20]
64/24,
8/3,
8:3 ANS
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
[U*8*48/60] = [V*4] [BECAUSE 1 MINUTE=60SECONDS]
[U*8*4/5] = [4V]
[U*44/5] = [4V]
44/5 U = 4V
THEN, USE THE FORMULA-----If the speed of the boat in still water is U km/hr and the stream of the boat is V km/hr then.
speed downstream = (u+v)km/hr
speed up stream = (u+v)km/hr
so, our U= 44/5 COME AND V= 4 COME
NOW, [U+V]/[U-V]
[44/5+4] / [44/5-4]
[44+20] / [44-20]
64/24,
8/3,
8:3 ANS
Aparna said:
1 decade ago
We all know this basic rule of finding ratio which is:
x/y = a/b.
Further when we solve this, we get:
x+y/x-y = a+b/a-b .... equation (1).
Solution:
Let the boat's speed upstream be x & downstream be y.
Therefore,
According to the formula, Distance = Speed*Time.
We get for upstream, D= x*44/5.
& for downstream, D= x*4.
Now, in the question, it is given that the distance covered is same while going upstream and downstream.
Therefore,
x*44/5 = 4y.
x/y = 11/5 (satisfies the equation: x/y = a/b).
Now put this value of x/y in equation (1).
x+y/x-y = 11+5/11-5.
x+y/x-y = 16/6.
x+y/x-y = 8/3.
8:3 is the Answer.
x/y = a/b.
Further when we solve this, we get:
x+y/x-y = a+b/a-b .... equation (1).
Solution:
Let the boat's speed upstream be x & downstream be y.
Therefore,
According to the formula, Distance = Speed*Time.
We get for upstream, D= x*44/5.
& for downstream, D= x*4.
Now, in the question, it is given that the distance covered is same while going upstream and downstream.
Therefore,
x*44/5 = 4y.
x/y = 11/5 (satisfies the equation: x/y = a/b).
Now put this value of x/y in equation (1).
x+y/x-y = 11+5/11-5.
x+y/x-y = 16/6.
x+y/x-y = 8/3.
8:3 is the Answer.
Rishikesh Agrawani said:
8 years ago
Let as assume,
The speed of boat is : b km/hr.
The speed of the water is : w km/hr.
In downstream the relative speed of the boat is: d = (b + w) km/hr.
In upstream the relative speed of the boat is : u = (b - w) km/hr.
According to the question,
The distance covered in upstream = (b + w) *4 km.
The distance covered in downstream = (b - w) * (8 + 48/60) km.
As the distance covered by boat is same in both direction, Hence.
(b + w) *4 = (b - w) *8.8.
(b*8.8) - (b*4) = (w*4 + w*8.8).
b*4.8 = w*12.8.
b/w = 8/3.
Or b:w = 8:3.
The speed of boat is : b km/hr.
The speed of the water is : w km/hr.
In downstream the relative speed of the boat is: d = (b + w) km/hr.
In upstream the relative speed of the boat is : u = (b - w) km/hr.
According to the question,
The distance covered in upstream = (b + w) *4 km.
The distance covered in downstream = (b - w) * (8 + 48/60) km.
As the distance covered by boat is same in both direction, Hence.
(b + w) *4 = (b - w) *8.8.
(b*8.8) - (b*4) = (w*4 + w*8.8).
b*4.8 = w*12.8.
b/w = 8/3.
Or b:w = 8:3.
Kanchan said:
4 years ago
By using the formula we have;
Speed upstream = u-v.
Speed downstream= u+v.
Where u&v is speed of the boat in still water and speed of stream respectively.
Given that distance covered is equal so;
By the time distance formula;
Speed *time= distance.
Both the values put according to formula.
(u-v) *8*48/60=(u+v) 4.
(u-v) 8*4/5=(u+v) 4.
44/5u-44/5v= 4u+4v.
44/5u- 4u = 44/5v+4v.
u[44/5-4] = v[44/5+4].
24u = 64v.
u/v = 64/24.
u/v = 8/3.
So, the ratio between the speed of the boat and speed of the water current is;
8:3.
Speed upstream = u-v.
Speed downstream= u+v.
Where u&v is speed of the boat in still water and speed of stream respectively.
Given that distance covered is equal so;
By the time distance formula;
Speed *time= distance.
Both the values put according to formula.
(u-v) *8*48/60=(u+v) 4.
(u-v) 8*4/5=(u+v) 4.
44/5u-44/5v= 4u+4v.
44/5u- 4u = 44/5v+4v.
u[44/5-4] = v[44/5+4].
24u = 64v.
u/v = 64/24.
u/v = 8/3.
So, the ratio between the speed of the boat and speed of the water current is;
8:3.
(1)
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