Multiple choice

Gyani goes to his coaching institute from his home at a speed of 3 kmph and returns at a speed of 2 kmph. If he takes 5 hours in all, then find the distance (in kms) between the coaching institute and Gyani's home.

  1. 6 km

  2. 5 km

  3. 4 km

  4. 12 km
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A Correct answer
Explanation

Let distance be D. Time = D/3 + D/2 = 5. D(1/3 + 1/2) = 5. D(5/6) = 5. D = 6 km.

AI explanation

Using the formula for equal distances, the average speed for the whole journey is 2xy/(x+y), where x is 3 kmph and y is 2 kmph. The average speed becomes 2*3*2/(3+2) = 12/5 kmph. Since the total time taken is 5 hours, the total distance is (12/5)*5 = 12 km. The distance between the coaching institute and the home is half of this total distance, which is 6 km.

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