Multiple choice

A man reaches his office 5 minutes late when he travels at the speed of 8 kmph. However, when he increases his speed to 12 kmph, he reaches 5 minutes early. What is the distance that he travels?

  1. 4 km

  2. 6 km

  3. 10 km

  4. Cannot be determined

  5. None of these
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A Correct answer
Explanation

Let d be the distance. Time difference is 10 minutes (5 late + 5 early) = 1/6 hour. d/8 - d/12 = 1/6. (3d - 2d)/24 = 1/6, so d/24 = 1/6, d = 4 km.

AI explanation

Let the distance to the office be D kilometers and the exact required time be T hours. Using the formula time equals distance divided by speed, the first condition gives D divided by 8 equals T plus 5/60, and the second gives D divided by 12 equals T minus 5/60. Subtracting the second equation from the first eliminates T, resulting in D/8 - D/12 = 10/60, which simplifies to D/24 = 1/6. Solving this gives D equals 4, so the distance traveled is 4 km.

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