Multiple choice

A boat covers 80 km downstream and 60 km upstream in 25 hours. If speed of current of river is 50% of its upstream speed, then in what time will it cover a distance of 120 km downstream and 100 km upstream?

  1. 40 hours

  2. 50 hours

  3. 25 hours

  4. 45 hours

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

Let boat speed = b, current = c. Upstream speed = b-c. Current c = 0.5(b-c) => 2c = b-c => b = 3c. Upstream = 2c, Downstream = 4c. 80/4c + 60/2c = 25 => 20/c + 30/c = 25 => 50/c = 25 => c = 2. Downstream = 8, Upstream = 4. Time = 120/8 + 100/4 = 15 + 25 = 40 hours.

AI explanation

Let the upstream speed of the boat be u, making the speed of the current 0.5u and the downstream speed 1.5u. Using the basic formula time equals distance divided by speed, the first condition gives the equation 80/(1.5u) + 60/u = 25, which simplifies to u = 4. The required time is found by substituting this speed into the expression 120/(1.5u) + 100/u, yielding 120/6 + 100/4. The sum of 20 and 25 is 45 hours, so the total time taken is 45 hours.

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