Multiple choice

A person travels from his house to office using cycle in 2 hrs 30 minutes and from office to industry using company car at a speed 75 km/hr. The ratio of distances is 2: 9. The average speed is 50 km/hr. Find the speed of the cycle.

  1. 37.5 m/sec

  2. 20 km/hr

  3. 37.5 km/hr

  4. 20 m/sec

  5. 15 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance to office be 2x and to industry be 9x. Total distance = 11x. Total time = 2.5 + (9x/75). Average speed = Total distance / Total time = 11x / (2.5 + 9x/75) = 50. Solving for x gives x = 25. Time for cycle = 2.5 hours, distance = 2*25 = 50 km. Speed = 50/2.5 = 20 km/hr.

AI explanation

Let the cycle distance be 2x km and the car distance be 9x km, making the total distance 11x km. Given the average speed of 50 km/hr, the total time taken for the entire journey is 11x divided by 50 hours. Since the car travel time is 9x/75 hours and the cycle time is 2.5 hours, we set 2.5 + (9x/75) = 11x/50, which simplifies to 2.5 = x/10, yielding x = 25. The cycle speed is the cycle distance of 50 km divided by 2.5 hours, resulting in 20 km/hr.

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