Multiple choice

A motor boat, whose speed is p km./hr. in still water goes 30 km downstream and comes back in a total of 4 hour and 30 minutes. The speed of the stream is 5 kmph. Find the value of p. एक मोटरबोट जिसकी चाल स्थिर जल में p किमी./घण्टा है, 30 किमी. अनुप्रवाह जाती है और कुल 4 घण्टे 30 मिनट में वापस आ जाती है। धारा की चाल 5 किमी./घण्टा है। p का मान ज्ञात कीजिए।

  1. 8 kmph/किमी./घण्टा

  2. 10 kmph/किमी./घण्टा

  3. 12 kmph/किमी./घण्टा

  4. 15 kmph/किमी./घण्टा
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D Correct answer
Explanation

Downstream speed = p+5, upstream speed = p-5. Time equation: 30/(p+5) + 30/(p-5) = 4.5 hours. Simplifying gives: 60p/(p²-25) = 4.5, leading to 3p² - 40p - 75 = 0. Solving: p = [40 ± √(1600+900)]/6 = [40 ± 50]/6. Positive solution: p = 90/6 = 15 kmph. The negative solution is discarded as speed cannot be negative.

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