Question : The speed of a boat in still water is $5 \frac{1}{3} \mathrm{~km} / \mathrm{hr}$. It is found that the boat takes thrice as much time to row up as it does to row down the same distance in the river stream. Find the speed of the river stream.
Option 1: $\frac{23}{27}$ m/sec
Option 2: $\frac{22}{27}$ m/sec
Option 3: $\frac{20}{27}$ m/sec
Option 4: $\frac{19}{27}$ m/sec
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Correct Answer: $\frac{20}{27}$ m/sec
Solution :
Given, The speed of a boat in still water = $5 \frac{1}{3}$ km/hr = $\frac{16}{3}$ km/hr
Let the speed of the stream be $x$ km/hr.
Let the time taken to row along the stream $t$ hours.
Then, the time taken to row against the stream = $3t$ hours
According to the question,
$(\frac{16}{3}+x)\times t=(\frac{16}{3}-x)\times 3t$
⇒ $\frac{16}{3}+x=16-3x$
⇒ $4x=\frac{32}{3}$
⇒ $x=\frac{8}{3}$ km/hr
⇒ $x=\frac{8}{3}\times \frac{5}{18}$ m/sec
⇒ $x=\frac{20}{27}$ m/sec
Hence, the correct answer is $\frac{20}{27}$ m/sec.
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