Boats and streams use the concept of relative speed, where we have one moving object on a surface which is in motion.
In this case, Speeds are added when moving in the same direction, and subtracted when moving in the opposite direction.
In the question above, we are given that for every 4 kms traveled downstream, he moves 3 kms upstream i.e the ratio of speeds \(S_d : S_u = 4 : 3\).
Let \(S_d = 4x\) and \(S_u = 3x\)
\(Total \space Time = \frac{d_u}{S_u} + \frac{d_d}{S_d}\)
\(14 = \frac{48}{4x} + \frac{48}{3x} = \frac{12}{x} + \frac{16}{x} = \frac{28}{x}\)
Therefore x = 2.
Substituting for x, \(S_d = 8\) and \(S_u = 6\)
\(S_s = \frac{S_d \space - \space S_u}{2}= \frac{8 - 6}{2} = 1\)
Option AIt is good to remember to derive the equations when doing questions on Boats and Streams
There are 4 equations based on this.
If \(S_b\) is the Speed of Boat in still water and \(S_s\) is the speed of the stream, then
Speed Downstream, \(S_d = S_b \space + \space S_s\) .... (1)
Speed Upstream, \(S_d = S_b \space - \space S_s\) ..... (2)
Adding Equations (1) and (2), we get \(S_b = \frac{S_d \space + \space S_u}{2}\) ... (3)
Subtracting the Equations, we get \(S_s = \frac{S_d \space - \space S_u}{2}\) ... (4)
Arun Kumar
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Crackverbal Prep Team
www.crackverbal.com