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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Question : A boat goes 12 km downstream and comes back to the starting point in 3 hours. If the speed of the current is 3 km/h, then the speed (in km/h) of the boat in still water is:
Option 1: 12
Option 2: 9
Option 3: 8
Option 4: 6
Question : A boat goes 2 km upstream and 3 km downstream in 20 minutes. It goes 7 km upstream and 2 km downstream in 53 minutes. What is the speed (in km/hr) of the boat in still water?
Option 1: $\frac{75}{7}$
Option 2: $\frac{120}{7}$
Option 3: $\frac{135}{7}$
Option 4: $\frac{150}{7}$
Question : A boat goes 75 km upstream in 3 hours and 60 km downstream in 1.5 hours. The speed of the boat in still water is:
Option 1: 32.5 km/h
Option 2: 30 km/h
Option 3: 65 km/h
Option 4: 60 km/h
Question : A speedboat, whose speed is 20 km/hr in still water, goes 35 km downstream and comes back in a total of 8 hours. What is the speed of the stream?
Option 1: 20 km/hr
Option 2: 10 km/hr
Option 3: 15 km/hr
Option 4: 5 km/hr
Question : A boat can go 40 km downstream and 25 km upstream in 7 hours 30 minutes. It can go 48 km downstream and 36 km upstream in 10 hours. What is the speed (in km/hr) of the boat in still water?
Option 1: 6
Option 2: 12
Option 3: 9
Option 4: 15
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