Multiple choice

The ratio of speed of boat in still water to speed of stream is 8 : 5 and total time taken by boat to cover 'D' km distance in downstream and upstream together is 32 hours. Find the time taken by boat to cover '2D' km in still water?

  1. 13 hour

  2. 14.8 hour

  3. 19.5 hour

  4. 12.78 hour

  5. 20.7 hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = 8k, stream = 5k. Downstream = 13k, Upstream = 3k. D/13k + D/3k = 32. D(3+13)/(39k) = 32 => 16D/39k = 32 => D/k = 78. Time for 2D in still water = 2D / 8k = D/4k = 78/4 = 19.5 hours.

AI explanation

Let the speed of the boat in still water be 8x and the speed of the stream be 5x, making the downstream speed 13x and the upstream speed 3x. Using the formula Time = Distance / Speed, the total time is (D / 13x) + (D / 3x) = 32 hours, which simplifies to 16D / 39x = 32, giving D / x = 78. To find the time to cover 2D in still water, calculate 2D / 8x = 2/8 × (D/x) = 1/4 × 78 = 19.5 hours.

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