Multiple choice

A motor boat goes 2 km upstream in a stream flowing at the rate of 3 km per hour and then returns downstream to the starting point in 30 minutes. Find the speed of the motor boat in still water. एक मोटर बोट 2 किमी. ऊर्ध्वप्रवाह में 3 किमी.प्रति घंटे की चाल से गति करती है और फिर अनुप्रवाह में गति करते हुए मूल बिंदु पर 30 मिनट में पहुँचती है। स्थिर जल में मोटर बोट की चाल ज्ञात कीजिये।

  1. 9.5 kmph/किमी./घंटा

  2. 8.5 kmph/किमी./घंटा

  3. 9 kmph/किमी./घंटा

  4. 8 kmph/किमी./घंटा
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C Correct answer
Explanation

Let boat speed in still water = b kmph. Stream speed = 3 kmph. Upstream speed = b - 3, time = 2/(b-3) hours. Downstream speed = b + 3, time = 2/(b+3) hours. Total time = 30 min = 0.5 hours. So 2/(b-3) + 2/(b+3) = 0.5. Solving: 4b/(b²-9) = 0.5, so 8b = b² - 9, giving b² - 8b - 9 = 0. So b = 9 kmph (ignoring negative solution).

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