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
Correct Answer: 9
Solution : Speed of the current, y = 3 km/h Let the speed of the boat in still water be $x$ km/h. According to the question, $\frac{12}{x+3}+\frac{12}{x-3} =3$ ⇒ $12(\frac{x-3+x+3}{(x+3)(x-3)})$ = 3 ⇒ $4\times 2x = x^2 - 9$ ⇒ $x^2 -8x-9 = 0$ ⇒ $x^2-9x+x-9 = 0$ ⇒ $x(x-9)+1(x-9) = 0$ ⇒ $(x+1)(x-9) = 0$ We get two values of $x$ as –1 and 9. The speed of the boat can not be –1. Hence, the correct answer is 9 km/h.
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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 boat covers a distance of 72 km downstream in 6 hours, while it takes 12 hours to cover the same distance upstream. What is the speed of the boat in still water?
Option 1: 6 km/hr
Option 2: 9 km/hr
Option 3: 10 km/hr
Option 4: 8 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
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 : 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
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