Multiple choice

Ratio of the time taken by the boat travel 150 km against stream to time taken to covers the same distance along with stream is 5: 1. If the speed of the stream is 20 kmph, then what is the speed of boat in still water?

  1. 40 kmph

  2. 25 kmph

  3. 30 kmph

  4. 45 kmph

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v be the boat speed and s=20 be the stream speed. The time ratio (distance/(v-s)) / (distance/(v+s)) = 5/1 simplifies to (v+s)/(v-s) = 5/1. Solving v+20 = 5(v-20) gives v+20 = 5v-100, so 4v = 120 and v = 30 kmph.

AI explanation

Let the speed of the boat in still water be x kmph. Since time is inversely proportional to speed, the ratio of the upstream speed (x minus 20) to the downstream speed (x plus 20) is 1:5. Cross-multiplying the equation (x minus 20) divided by (x plus 20) equals 1 divided by 5 gives 5x minus 100 equals x plus 20. Solving this yields 4x equals 120, so the speed of the boat in still water is 30 kmph.

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