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A man rows a boat such that it covers a distance upstream in twice the time taken by him to cover the same distance downstream. If the speed of stream is 5 km/h, the speed of boat in still water is:

Solution

Correct Option: 3

Let the speed of boat in still water = bb km/h

Speed of stream = 5 km/h

When rowing in a stream:

  • Upstream speed = (b5)(b - 5) km/h
  • Downstream speed = (b+5)(b + 5) km/h

For the same distance dd:

Time upstream = db5\dfrac{d}{b - 5}

Time downstream = db+5\dfrac{d}{b + 5}

Given that time upstream is twice the time downstream:

db5=2×db+5\dfrac{d}{b - 5} = 2 \times \dfrac{d}{b + 5}


Canceling dd from both sides:

1b5=2b+5\dfrac{1}{b - 5} = \dfrac{2}{b + 5}

b+5=2(b5)b + 5 = 2(b - 5)

b+5=2b10b + 5 = 2b - 10

5+10=2bb5 + 10 = 2b - b

b=15b = 15


Therefore, the speed of boat in still water is 15 km/h.

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