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The ratio of the speed of a boat in still water to the speed of the stream is 5 ∶ 1, if a man can row a distance of 120 km upstream in 2 hrs more than the time taken to travel the same distance downstream, find the speed of boat in still water?
1. 12 km/hr
2. 18 km/hr
3. 25 km/hr
4. 20 km/hr
5. 21 km/hr

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Correct Answer - Option 3 : 25 km/hr

Given

The ratio of the speed of the boat in still water to speed is stream is 5 ∶ 1

Formula used

Let u and v be the speed of the boat in still water and speed of stream respectively.

Speed upstream = (u - v)

Speed downstream = (u + v)

Calculations

Let the speed of the boat in still water be 5x and the speed of the stream be 1x

Speed while travelling downstream = (u + v) km / hr

⇒ 5x + 1x = 6x

Speed while travelling upstream = (u - v) km / hr

⇒ 5x - 1x = 4x

According to question

⇒ Time(upstream) - Time(downstream) = 2 hr

\(⇒ \frac{{120}}{{4x}} - \frac{{120}}{{6x}} = 2\)        ---(1)

On solving the above equation; we get x = 5

Speed of the boat in still water is 5x = 5 × 5

⇒ 25 km / hr

Hence the speed of the boat in still water is 25 km/hr.

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