Multiple choice

Passage

Directions: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You are to use the given data and your knowledge of Mathematics to choose among the given options.

Quantity I: The distance from point A to B is 156 km and a ferry takes a round trip and completes the same in 12 hours and 30 minutes. It is given that the ratio of the speed of the ferry in still water to the stream speed is 8 : 5. Calculate the speed of the ferry in still water. Quantity II: Roger travels at the speed of 84 km/hr for 6 hours and at 72 km/hr for 4 hour. Calculate his average speed for the journey of 10 hours.

  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 can be established.
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A Correct answer
Explanation

Quantity I: Round trip distance = 312 km. Total time = 12.5 hours. Let speed in still water be 8x and stream be 5x. Downstream = 13x, Upstream = 3x. 156/13x + 156/3x = 12.5 => 12/x + 52/x = 12.5 => 64/x = 12.5 => x = 5.12. Still water speed = 8 * 5.12 = 40.96 km/h. Quantity II: Average speed = Total distance / Total time = (84*6 + 72*4) / 10 = (504 + 288) / 10 = 79.2 km/h. Thus, I < II.

AI explanation

For Quantity I, let the speed of the ferry in still water be 8x and the stream speed be 5x. Using the total round trip time of 12.5 hours, we write 156 divided by 13x plus 156 divided by 3x equals 12.5, which solves to x equals 3.6, making the ferry's speed in still water 28.8 km/hr. For Quantity II, the average speed is the total distance divided by the total time, giving 84 times 6 plus 72 times 4 divided by 10, which equals 79.2 km/hr. Comparing the two, Quantity I is less than Quantity II.

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