Multiple choice

Directions: In the following question, two quantities are given numbered I and II. Determine the relationship between the quantities and choose the appropriate option. Quantity I: The average speed (in kmph) over the distance, if a car covers four successive 20 km stretches at the speeds of 10 km/hr, 20 km/hr, 30 km/hr and 40 km/hr, respectively Quantity II: The average speed (in kmph) over the distance, if a bus travels the distances of 30 km, 80 km and 40 km at the speeds of 15 km/hr, 20 km/hr and 10 km/hr, respectively

  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 the relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Total distance = 80 km. Time = 20/10 + 20/20 + 20/30 + 20/40 = 2 + 1 + 2/3 + 1/2 = 3 + 4/6 + 3/6 = 3 + 7/6 = 25/6 hours. Average speed = 80 / (25/6) = 480/25 = 19.2 km/hr. Quantity II: Total distance = 30 + 80 + 40 = 150 km. Time = 30/15 + 80/20 + 40/10 = 2 + 4 + 4 = 10 hours. Average speed = 150/10 = 15 km/hr. Since 19.2 > 15, Quantity I > Quantity II.

AI explanation

For Quantity I, we use the Harmonic Mean formula for equal distances, where the average speed is 4 divided by the sum of the reciprocals of the speeds (1/10 + 1/20 + 1/30 + 1/40). This yields an average speed of 19200 divided by 275, which is approximately 69.8 kmph. For Quantity II, the total distance of 150 km is divided by the sum of the times (30/15 + 80/20 + 40/10), which equals 9 hours, giving an average speed of 150 divided by 9 equals 16.67 kmph. Therefore, Quantity I is greater than Quantity II.

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