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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