Question : The speed of the current is 5 km/h. A motorboat goes 10 km upstream and back again to the starting point in 50 minutes. The speed (in km/h) of the motorboat in still water is:
Option 1: 20
Option 2: 26
Option 3: 25
Option 4: 28
Correct Answer: 25
Solution :
Let the speed of the boat be $x$ km/h.
Given: The speed of current = 5 km/h
Therefore, upstream speed of boat = $(x-5)$ km/h
Downstream speed of the boat = $(x + 5)$ km/h
According to the question,
$ \frac{10}{x-5}+\frac{10}{x+5}=\frac{50}{60} $
⇒ $10 \left(\frac{x+5+x-5}{x^{2}-25}\right)=\frac{5}{6}$
⇒ $12 \times 2x = x^{2}-25$
⇒ $x^{2}-24x-25=0$
⇒ $x^{2}-25x+x-25=0$
⇒ $\left(x-25\right) \left(x+1\right)=0$
Therefore, $x = 25$ (Since the speed of the boat can not be negative)
Hence, the correct answer is 25.
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