Multiple choice

Directions: In the following question, we have two quantities given. Compare these quantities and answer accordingly with the following given options. Quantity I: Kiran goes to his friend's house by car at a speed of 40 km/hr and reaches 10 minutes early. If he goes at a speed of 30 km/hr, he reaches 12 minutes late. The distance to his friend's house. Quantity II: 50 km

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D. Time at 40 km/hr = D/40. Time at 30 km/hr = D/30. Difference in time = 12 min late - (-10 min early) = 22 minutes = 22/60 hours. D/30 - D/40 = 22/60. (4D - 3D)/120 = 22/60. D = 120 * (22/60) = 44 km. Since 44 < 50, Quantity I < Quantity II.

AI explanation

Using the standard formula where distance equals the product of the two speeds and the sum of the time differences, divided by the difference of the speeds, we calculate the distance. The time difference is 10 minutes early plus 12 minutes late, totaling 22 minutes, which is 11/30 hours. Distance equals (40 multiplied by 30 multiplied by 11/30) divided by (40 - 30), resulting in 44 km. Since 44 km is less than the 50 km in Quantity II, Quantity I < Quantity II.

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