Question : A man rows to a place situated 100 km away and comes back in 10 hours. He can row 12 km downstream or 8 km upstream in the same time. What is the speed of the stream?
Option 1: $\frac{20}{9}$ km/hr
Option 2: $\frac{23}{8}$ km/hr
Option 3: $\frac{29}{5}$ km/hr
Option 4: $\frac{25}{6}$ km/hr
Correct Answer: $\frac{25}{6}$ km/hr
Solution :
Let's denote the speed of the man in still water as M (in km/h) and the speed of the stream as S (in km/h).
So, speed in upstream = M − S
and, speed in downstream = M + S
According to the question,
$\frac{100}{M + S}$ + $\frac{100}{M - S}$ =10
Also, $\frac{12}{M+S}$ = $\frac{8}{M - S}$
⇒ $12(M − S) = 8(M +S)$
⇒ $4M = 20S$
⇒ $M = 5S$
Now put this value in 1st relation
⇒ $\frac{100}{5S+S}$ + $\frac{100}{5S−S}$ = 10
⇒ $\frac{100}{6S}$ + $\frac{100}{4S}$ = 10
⇒ $\frac{50}{3S}$ + $\frac{25}{S}$ = 10
⇒ $\frac{125}{3S}$ = 10
⇒ $S=\frac{25}{6}$
Hence, the correct answer is $\frac{25}{6}$ km/hr.
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