Question : A boat covers a certain distance against the stream in 9 hours 36 min and it covers the same distance along the stream in 6 hours. What is the ratio of the speed of the boat in still water to that of the stream?
Option 1: 13 : 3
Option 2: 9 : 2
Option 3: 11 : 6
Option 4: 8 : 5
Correct Answer: 13 : 3
Solution :
Let the speed of the boat in still water and the speed of the stream be $x$ and $y$ km/hr.
Time taken by boat to cover some distance along the stream = 6 hours
Time taken by boat to cover the same distance against the stream = 9 hours 36 min = 9.6 hours
Speed of water along the stream = $x+y$ km/hr
Speed of water against the stream = $x-y$ km/hr
We know, Distance = Speed × Time
According to the question,
$6(x+y)=9.6(x-y)$
⇒ $15.6y = 3.6x$
⇒ $\frac{x}{y}=\frac{15.6}{3.6}$
⇒ $\frac{x}{y}=\frac{13}{3}$
Hence, the correct answer is 13 : 3.
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