Multiple choice

Ram travels from P to Q at 10 km/hr and returns at 15 km/hr Shyam travels from P to Q and returns at 12.5 km/hr If he takes 12 minutes less than Ram then what is the distance between P and Q?

  1. 60 km

  2. 45 km

  3. 36 km

  4. 30 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be D. Ram's time = D/10 + D/15 = D/6. Shyam's time = D/12.5 + D/12.5 = 2D/12.5 = D/6.25. Difference = D/6.25 - D/6 = 12/60 hours = 0.2 hours. (6D - 6.25D) / 37.5 = 0.2. 0.25D = 7.5. D = 30 km.

AI explanation

Let the distance between P and Q be d km; using the formula time equals distance divided by speed, Ram's total time is d/10 + d/15 and Shyam's total time is 2d/12.5. The difference in time is 12 minutes or 0.2 hours, giving the equation d/10 + d/15 - 2d/12.5 = 0.2. Finding a common denominator for the left side yields (3d + 2d)/30 - 2d/12.5 = 0.2, which simplifies to d/6 - 2d/12.5 = 0.2; solving this gives d = 30 km.

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