Multiple choice

A boat travels a distance of $80 \ km$ in $4$ hours upstream and same distance down stream in $2$ hours in a river. Then the velocities of boat and stream are (in Kmph)

  1. $20, 10$
  2. $30, 10$
  3. $30, 20$

  4. None of these
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B Correct answer
Explanation

Upstream speed = 80 / 4 = 20 km/h. Downstream speed = 80 / 2 = 40 km/h. Let boat speed be v and stream speed be s. v - s = 20 and v + s = 40. Adding these gives 2v = 60, so v = 30. Then s = 10.

AI explanation

Using the formula speed equals distance divided by time, the upstream speed is 80 divided by 4, giving 20 kmph, and the downstream speed is 80 divided by 2, giving 40 kmph. The velocity of the boat in still water is the average of these speeds, so (20 + 40) divided by 2 yields 30 kmph. The stream velocity is half the difference of these speeds, meaning (40 - 20) divided by 2 yields 10 kmph. The velocities of the boat and stream are 30 and 10.

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