CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

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 the speed of the water current respectively?


A

2:1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

3:2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

8:3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

3:8

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

8:3


Step 1: Given data

The distance covered upstream in Tu=8hrs48min is equal to the distance covered downstream in Td=4hrs.

Step 2: Formula used

  1. If the speed downstream is ykm/hrand the speed upstream is xkm/hr, then:
  2. The speed of the boat is given by sb=12(downstreamspeed+upstreamspeed)=x+y2
  3. The speed of the water stream is given by sw=12(downstreamspeed-upstreamspeed)=y-x2

[ where x= speed of the boat upstream and y= the speed of the boat downstream ]

Step 3: Calculating the speed of the boat upstream and the speed of the downstream

Suppose the speed of the boat upstream is x km/hr and the speed for the downstream is y km/hr.


Now, by using the given data we get the equation as multiplication of speed for downstream to its time and multiplication of upstream speed with its time as:

x×Tu=y×Tdx×84860=y×4

Then, we will solve the above expression to get the value of the ratio x:y as:

845x=4y445x=4yxy=4×544xy=511

Step 4: Calculating the ratio between the speed of the boat and the speed of the water

Dividing the speed of the boat with the speed of the water current to get the ratio as:

sbswx+y2y-x2x+yy-x

Divide the numerator and denominator by y to get the required ratio as:

xy+11-xy

Substituting the value of xy=511

511+11-5115+111111-51116683

So, we get the ratio between the speed of the boat and the speed of the water current respectively as 8:3.
Hence, option (c) is the correct answer.


flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image