Multiple choice

Two quantities that is I and II are given in following questions. Students are expected to solve the quantities and answer them according to given options by comparing their numerical values. The time taken by a motorboat to travel 2100 km upstream is 80 hours more than the time taken by it to travel the same distance in downstream. The speed of the motorboat in still water is 500% more than that the speed of stream. Quantity I: How much time the motorboat will take to travel the same distance in upstream? Quantity II: How much time the motorboat will take to travel 3000 km downstream if due to wind, the speed of stream was increased by 20%?

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or no relation
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A Correct answer
Explanation

Let stream speed = x, then boat speed = 6x (500% more). Downstream speed = 7x, upstream speed = 5x. Time difference: 2100/5x - 2100/7x = 80. Solving gives x = 100 km/hr, boat speed = 600 km/hr. Quantity I: Upstream time = 2100/500 = 4.2 hours. Quantity II: New stream speed = 120 km/hr (20% increase). New downstream speed = 720 km/hr. Time for 3000 km = 3000/720 = 4.167 hours. Comparing 4.2 hours with 4.167 hours: 4.2 > 4.167.

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