Multiple choice

A boat goes at 6 km. upstream and back again to starting point in 2 hours. If the speed of the current in 4 km./hr., what is the speed of the boat in still water? एक नाव धारा के प्रतिकूल 6 किमी. जाकर उसी प्रारम्भिक स्थान पर 2 घंटे में वापस आ जाती है। यदि धारा की चाल 4 किमी./घं. है तो शान्त जल में नाव की चाल क्या है?

  1. 4 km./hr.

  2. 6 km./hr.

  3. 8 km./hr.

  4. 12 km./hr.
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C Correct answer
Explanation

Let boat speed in still water be b km/hr. Upstream speed = b-4, downstream speed = b+4. Total time: 6/(b-4) + 6/(b+4) = 2 hours. Solving: 6(b+4+b-4) = 2(b²-16), so 12b = 2b²-32, giving b²-6b-16=0. Factorizing: (b-8)(b+2)=0. Therefore b=8 km/hr (speed cannot be negative).

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