Multiple choice

Travelling at a speed of 20 km/hr, a person reaches his office 10 minutes late. If he travels at a speed of 30 km/hr, he reaches his office 10 minutes early. How far is his office from his house?

  1. 10 km

  2. 20 km

  3. 25 km

  4. 30 km

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D. Time taken at 20 km/hr is D/20, and at 30 km/hr is D/30. The difference in time is 20 minutes (10 minutes late vs 10 minutes early), which is 1/3 hour. Solving D/20 - D/30 = 1/3 gives D/60 = 1/3, so D = 20 km.

AI explanation

Let the correct time to reach the office be t hours. Since the distance travelled in both cases is the same, using the formula distance = speed into time gives 20 multiplied by (t + 10/60) = 30 multiplied by (t minus 10/60). Solving this equation gives 20t + 10/3 = 30t minus 5, which results in 10t = 15/3 or t = 0.5 hours. Plugging this back into the first scenario, the distance equals 20 multiplied by (0.5 + 10/60), which equals 20 multiplied by 2/3, resulting in a distance of 20 km.

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