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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