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:
109 comments Page 4 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.
Swapna said:
7 years ago
Thank you @Bindu.
Pavan chennur said:
7 years ago
Distance is constant. So that we have a relationship between speed and time.
SAGOR said:
7 years ago
Let, the distance be = d.
Downsream speed= d/4,
Upstream speed= 5d/44,
So, d/4 : 5d/44.
11: 5.
Now, the speed of the boat =(11+5)/2.
= 8.
The speed of the current =(11-5)/2.
= 3.
So, ratio 8:3.
Downsream speed= d/4,
Upstream speed= 5d/44,
So, d/4 : 5d/44.
11: 5.
Now, the speed of the boat =(11+5)/2.
= 8.
The speed of the current =(11-5)/2.
= 3.
So, ratio 8:3.
(1)
RAMJAN said:
7 years ago
I got the value of x+y/2 =13x4 instead of 16x/10.
Am I correct?
Am I correct?
Ronie said:
7 years ago
First convert Hours to Mins.
8hrs 48mins= 528mins & 4hrs= 240mins.
Speed Down =x/528,
Speed Up=x/240,
Speed of stream =(x/240-x/528)÷2=x/880,
Speed of boat= x/240-x/880 =x/330,
Ratio=(x/330)/(x/880)= 8:3.
8hrs 48mins= 528mins & 4hrs= 240mins.
Speed Down =x/528,
Speed Up=x/240,
Speed of stream =(x/240-x/528)÷2=x/880,
Speed of boat= x/240-x/880 =x/330,
Ratio=(x/330)/(x/880)= 8:3.
Hari said:
7 years ago
Anyone explain me to get the answer.
Pratiksha said:
7 years ago
How that 8:3 ratio comes? Please anyone help me.
Dhiraj Take said:
7 years ago
@Deena R:.
Divide numerator and denominatr by 12.
Divide numerator and denominatr by 12.
Deena.r said:
7 years ago
How ll can the 48/60 =4/5? Please explain why?
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