Multiple choice

Passage

Directions: In the following question, two quantities are given numbered I and II. Determine the relationship between the quantities and choose the appropriate option. Give answer according to these codes: (1) If Quantity I ≥ Quantity II (2) If Quantity I > Quantity II (3) If Quantity I < Quantity II (4) If Quantity I ≤ Quantity II (5) If Quantity I = Quantity II, or the relationship cannot be established from the information given.

Quantity I: The speed of current, if a boat takes 6 hr to go a certain distance upstream but returns in just two hours and the speed of boat in still water is 4 kmph Quantity II: The speed of current, if the speed of a boat in still water is 10 kmph and it can travel 20 km downstream in the same time as it can travel 12 km upstream

  1. (3)

  2. (2)

  3. (1)

  4. (4)

  5. (5)
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A Correct answer
Explanation

Quantity I: Let boat speed be B=4 and current be C. Upstream speed is 4-C, downstream is 4+C. Distance D = (4-C)*6 = (4+C)*2. Solving gives 24-6C = 8+2C, so 8C=16, C=2. Quantity II: Let boat speed be 10 and current be C. 20/(10+C) = 12/(10-C). 200-20C = 120+12C, so 32C=80, C=2.5. Since 2 < 2.5, Quantity I < Quantity II.

AI explanation

For Quantity I, using the ratio of times for upstream and downstream (6 hours and 2 hours), the ratio of effective speeds is 1:3, meaning the speed of the current is half the upstream speed. Setting up the equation (4 minus c) multiplied by 6 equals (4 plus c) multiplied by 2 gives c equals 2 km/hr. For Quantity II, with the boat's speed at 10 km/hr and equal time for 20 km downstream and 12 km upstream, 20 divided by (10 plus c) equals 12 divided by (10 minus c), which solves to c equals 2.5 km/hr. Since 2 km/hr is less than 2.5 km/hr, Quantity I is less than Quantity II.

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