Multiple choice

A man cycles with a speed of 10 km/hr and reaches his office at 1 pm. However, when he cycles with a speed of 15 kmph, he reaches his office at 11 am. At what speed should he cycle so that he reaches his office at 12 noon? एक आदमी 10 किमी/घंटा की चाल से साइकिल चलाता है और दफ्तर 1 बजे अपराह्न पहुंचता है तथापि, जब वह 15 किमी/घंटा की चाल से साइकिल चलाता है तो वह पूर्वाह्न 11 बजे दफ्तर पहुंचता है। वह साइकिल कितनी चाल से चलाये कि अपने दफ्तर दोपहर 12 बजे पहुंचे ?

  1. 12 kmph/किमी/घंटा

  2. 10 kmph/किमी/घंटा

  3. 8 kmph/किमी/घंटा

  4. 20 kmph/किमी/घंटा
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A Correct answer
Explanation

Let distance = d and start time be t hours before 11 am. At 15 kmph, time taken = t hours. At 10 kmph, time taken = t + 2 hours (since 1 pm is 2 hours after 11 am). Distance is same, so 15t = 10(t + 2). Solving: 15t = 10t + 20, so 5t = 20, t = 4. Distance = 15 × 4 = 60 km. To reach at 12 noon (1 hour after 11 am), time needed = 4 + 1 = 5 hours. Speed = 60/5 = 12 kmph.

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