Multiple choice

The ratio of the speed of a boat in downstream direction to the speed of the stream is 12 : 1. If the speed of the stream is 3 km/hr, find the distance travelled upstream (in km) in 5 hours.

  1. 130

  2. 155

  3. 150

  4. 210

  5. 180
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C Correct answer
Explanation

Let speed of boat in still water be u and stream be v. Downstream speed = u + v. Given (u+v)/v = 12/1, so u+v = 12v. Given v = 3, so u+v = 36 km/hr. Upstream speed = u - v = (12v - v) - v = 10v = 30 km/hr. Distance = speed * time = 30 * 5 = 150 km.

AI explanation

Given the speed of the stream is 3 km/hr and the ratio of downstream speed to stream speed is 12:1, the downstream speed is 12 multiplied by 3, which equals 36 km/hr. Using the downstream speed formula, the boat's speed in still water is 36 minus 3, giving 33 km/hr. The upstream speed is the still water speed minus the stream speed: 33 minus 3 equals 30 km/hr. The distance traveled upstream in 5 hours is 30 multiplied by 5, which equals 150 km.

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