Question : The ratio of the speed of the boat in still water to the speed of the stream is 8 : 3 and the boat can travel 22 km downstream in 24 minutes. Then, how much time will the boat take to cover 50 km upstream?
Option 1: 4 hours
Option 2: 2.5 hours
Option 3: 3 hours
Option 4: 2 hours
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Correct Answer: 2 hours
Solution :
The ratio of the speed of the boat in still water to the speed of the stream is 8 : 3.
The boat can travel 22 km downstream in 24 minutes.
Let the speed of the boat in still water be 8x and the speed of the stream be 3x.
The speed of the boat in downstream = $\frac{22}{24}$ = $\frac{11}{12}$ km/min = $\frac{11}{12} \times{ 60}$ = 55 km/hr
The speed of the boat downstream = 8x + 3x = 11x
So, 11x = 55 km/hr
$\therefore$ x = 5 km/hr
The speed of the boat in still water = 8x = 40 km/hr
The speed of the boat upstream = 8x – 3x = 5x = 25 km/hr
$\therefore$ The time taken by the boat to cover 50 km upstream = $\frac{50}{25}$ = 2 hours
Hence, the correct answer is 2 hours.
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