Multiple choice

(\text{Find the value of quantities and state the correct relationship.}\\text{Quantity I: Speed of boat in still water if it took 24 hours to cover a distance of 64 km going downstream and back. Given the speed of current to be 2 km/hr} \\text{Quantity II: Average speed of a boy to go from home to school if his average speed is 2 km/hr from school to home and he covers a total of 12 km in 5 hours.})

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
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A Correct answer
Explanation

Quantity I: Let boat speed = b. Downstream (32 km) at b+2, upstream (32 km) at b-2. Total time 24 hours gives 32/(b+2) + 32/(b-2) = 24. Solving yields b = 4 km/hr. Quantity II: Total distance = 12 km in 5 hours gives average speed = 12/5 = 2.4 km/hr. Comparing: 4 > 2.4, so Quantity I > Quantity II.

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