Multiple choice

The distance between two points is 36 km. A boat rows in still water at 6kmph, it takes 8hr less to cover distance in downstream in comparison to that in upstream. Find the rate of stream. दो बिन्दुओं के बीच की दूरी 36 किमी. है | एक नाव स्थिर जल में 6 किमी./घंटा की चाल से तैर सकती है, यह दूरी को धारा के प्रवाह के अनुकूल तय करने में धारा के प्रतिकूल तय में लगे समय से 8 घंटे कम लेती है | धारा की चाल ज्ञात कीजिये |

  1. 4 kmph/किमी./घंटा

  2. 3 kmph/किमी./घंटा

  3. 2 kmph/किमी./घंटा

  4. 5 kmph/किमी./घंटा
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B Correct answer
Explanation

Let stream speed be x kmph. Downstream speed = 6 + x, upstream speed = 6 - x. Time downstream = 36/(6+x), time upstream = 36/(6-x). Given: 36/(6-x) - 36/(6+x) = 8. Multiplying by (6-x)(6+x): 36(6+x) - 36(6-x) = 8(36 - x²). This gives 36(6+x-6+x) = 8(36-x²), so 72x = 8(36-x²), or 9x = 36 - x². Rearranging: x² + 9x - 36 = 0, which gives (x+12)(x-3) = 0. Since speed can't be negative, x = 3 kmph.

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