Question : A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in $6\frac{1}{2}$ hours. The speed of the current is:
Option 1: 1 km/hr
Option 2: 2 km/hr
Option 3: 1.5 km/hr
Option 4: 2.5 km/hr
Correct Answer: 2 km/hr
Solution :
Given: Time taken by boat to cover 24 km upstream and 36 km downstream = 6 hours
Also, the time taken by boat to cover 36 km upstream and 24 km downstream = $6\frac{1}{2}$ hours
Let speed of boat in still water = $x$ km/hr
Speed of stream current = $y$ km/hr
According to the question,
$\frac{24}{x-y} +\frac{36}{x+y}=6$-----------$(i)$
$\frac{36}{x-y} +\frac{24}{x+y}=\frac{13}{2}$--------$(ii)$
Assume $\frac{1}{x-y}=a$ and $\frac{1}{x+y}=b$
So, the above two equations become,
$24a+36b=6$----------$(iii)$
and $36a+24b=\frac{13}{2}$-------$(iv)$
Solving these two equations, we get,
$a=\frac{1}{8}$ and $b=\frac{1}{12}$
So, $x-y=8$-----$(v)$ and $x+y=12$--------$(vi)$
Solving equation $(v)$ and $(vi)$, we get,
$⇒ x=10, y=2$
$\therefore$ Speed of stream current = 2 km/hr
Hence, the correct answer is 2 km/hr.
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