Multiple choice

A cyclist completes a certain journey in 7 hours. He covers half the distance at 12 km./hr and the second half of the distance at 9 km/hr. The distance (in km) covered by the cyclist is- एक साइकिल सवार कोई यात्रा 7 घंटे में पूरी करता है। वह आधी दूरी 12 किमी/घं. की चाल से तथा शेष आधी दूरी 9 किमी/घं की चाल से चलता है। साइकिल सवार द्वारा चली गई दूरी है (किमी. मे ) -

  1. 72

  2. 36

  3. 108

  4. 180

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A Correct answer
Explanation

Let total distance be d km. Time for first half = (d/2)/12 = d/24 hours. Time for second half = (d/2)/9 = d/18 hours. Total time: d/24 + d/18 = 7 hours. d(1/24 + 1/18) = 7, so d(7/72) = 7, giving d = 72 km. The harmonic mean of speeds for equal distances gives average speed = 2*12*9/(12+9) = 72/7 km/h. Distance = average speed × time = (72/7) × 7 = 72 km.