Processing math: 100%
About Us Services Blog Contact Us eBooks

A boat covers a round trip in a river in a certain time.If its speed in still water is doubled and the speed of the stream tripled it would take the same time for the round trip journey.Find the ratio of the speed of the boat in still water and the speed of the stream.

Question:

A boat covers a round trip in a river in a certain time.If its speed in still water is doubled and the speed of the stream tripled it would take the same time for the round trip journey.Find the ratio of the speed of the boat in still water and the speed of the stream.

Solution:

A boat covers a round trip in a river in a certain time.
Let the speed of boat in still water= x
Let speed of the stream = y
Let d be the one way distance.
So, total time taken by boat in round trip = time taken in downstream + time taken in upstream
total time for round trip =dx+y+dxy .....1
If its speed in still water is doubled ie 2x and the speed of the stream tripled ie 3y.
Total time for round trip=d2x+3y+d2x3y ....2
As time consumed same in the round trip journey.
From eqn 1 and 2
dx+y+dxy=d2x+3y+d2x3y
Cancel out d on both side.
1x+y+1xy=12x+3y+12x3y
(xy)+(x+y)(x+y)(xy)=(2x3y)+(2x+3y)(2x+3y)(2x3y)
2xx2y2=4x4x29y2
2x×(4x29y2)=4x×(x2y2)
8x318xy2=4x34xy2
8x34x3=4xy2+18xy2
4x3=14xy2
x3xy2=144
x2y2=144
x2y2=144
xy=142 on taking square root on both sides
Ratio of the speed of the boat in still water and the speed of the stream
x:y=14:2

Recent Posts

SBI Specialist Cadre Officer Recruitment 2024-25: Apply Now!

SBI Specialist Cadre Officer Recruitment 2024-25: Apply Now!

SBI Specialist Cadre Officer Recruitment 2024-25: Apply Now! body { font-family: sans-serif; line-height: 1.6; margin: 20px; } h1, h2, h3 { color: #333; } ul { list-style-type: disc; margin-left: 20px; } table { width: 100%; border-collapse: collapse; margin-top: 20px;

SBI Probationary Officer Recruitment 2024-25: Detailed Guide

SBI Probationary Officer Recruitment 2024-25: Detailed Guide

SBI Probationary Officer Recruitment 2024-25: Detailed Guide body { font-family: sans-serif; line-height: 1.6; margin: 20px; } h1, h2, h3 { color: #333; } ul { list-style-type: disc; margin-left: 20px; } table { width: 100%; border-collapse: collapse; margin-top: 20px; } th,