Multiple choice

Moving at 50 kmph, a person reaches his office 10 min late. Next day, he increases his speed and moves at 60 kmph and reaches his office 5 min early. What is the distance from his home to his office?

  1. 75 km

  2. 70 km

  3. 80 km

  4. 77 km
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A Correct answer
Explanation

Let distance be D. Time1 = D/50, Time2 = D/60. Time difference = 15 min = 1/4 hour. D/50 - D/60 = 1/4. (6D - 5D) / 300 = 1/4. D/300 = 1/4. D = 75 km.

AI explanation

Let the correct time to reach the office be t hours; the distance is constant, so using distance equals speed multiplied by time, 50 multiplied by (t + 10/60) equals 60 multiplied by (t - 5/60). Solving this equation gives 50t + 25/3 = 60t - 5, which simplifies to 10t = 40/3, so t is 4/3 hours. The distance to the office is 60 multiplied by (4/3 - 5/60), equaling 60 multiplied by 5/4, which results in 75 km.

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