Multiple choice

The ratio of time taken by a boat to cover a certain distance upstream to time taken by the boat to cover same distance downstream is 5 : 3. If the speed of stream is doubled, then the time taken by boat to cover a certain distance downstream will be what percent less than time taken by the boat to cover same distance in still water?

  1. 15

  2. 25.88

  3. 25

  4. 33.33

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

Let boat speed be b and stream speed be s. Upstream time/Downstream time = (b+s)/(b-s) = 5/3, so 3b+3s = 5b-5s, meaning 2b = 8s or b = 4s. If stream speed doubles to 2s, downstream time is d/(b+2s) = d/(4s+2s) = d/6s. Time in still water is d/b = d/4s. The percentage reduction is ((d/4s - d/6s) / (d/4s)) * 100 = (1/4 - 1/6) / (1/4) * 100 = (2/24) / (1/4) * 100 = 33.33%.

AI explanation

Let the boat's speed be b and the stream's speed be s; since the time ratio upstream to downstream is 5:3, the speed ratio is 3:5, meaning (b-s)/(b+s) = 3/5. Solving gives 5b - 5s = 3b + 3s, which simplifies to 2b = 8s and therefore b = 4s. If the stream's speed is doubled to 2s, the new downstream speed becomes 4s + 2s = 6s, whereas the still water time corresponds to a speed of 4s. Since time is inversely proportional to speed, the ratio of the new downstream time to the still water time is 4s/6s = 2/3, meaning the new time is 33.33 percent less.

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