Multiple choice

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities. Quantity I: The distance traveled by Rajesh in 61 hrs at the average speed for the entire trip if Rajesh rides his bike 20 km at average speed of 24 kmph and again travels 24 km at average speed of 20 kmph. Quantity II: The distance traveled by Pawan in 40 hrs at the average speed for the entire trip if Pawan covers a distance of 25 km at average speed of 30 kmph by his car and again travels 40 km at average speed of 25 kmph.

  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
A Correct answer
Explanation

Quantity I: Avg speed = Total Distance / Total Time. Time 1 = 20/24 = 5/6 hr. Time 2 = 24/20 = 6/5 hr. Total time = 5/6 + 6/5 = 61/30 hr. Total distance = 44 km. Avg speed = 44 / (61/30) = 1320/61 kmph. Distance in 61 hrs = (1320/61) * 61 = 1320 km. Quantity II: Time 1 = 25/30 = 5/6 hr. Time 2 = 40/25 = 8/5 hr. Total time = 5/6 + 8/5 = 73/30 hr. Total distance = 65 km. Avg speed = 65 / (73/30) = 1950/73 kmph. Distance in 40 hrs = (1950/73) * 40 = 78000/73 = 1068.49 km. Quantity I > Quantity II.

AI explanation

Using the harmonic mean formula for average speed, Rajesh's average speed for the entire 44 km trip is two times 24 times 20 divided by 24 plus 20, resulting in 480 by 11 kmph. Quantity I is this speed multiplied by 61 hours, which equals 2661.81 km. Using the same formula, Pawan's average speed for the 65 km trip is two times 30 times 25 divided by 30 plus 25, resulting in 300 by 11 kmph. Quantity II is this speed multiplied by 40 hours, which equals 1090.91 km. Therefore, Quantity I > Quantity II.

Keep practicing — related questions