Multiple choice

A boat goes 96 km upstream in 8 hours and covers the same distance moving downstream in 6 hours. On the next day boat starts from point A, goes downstream for 1 hour, then upstream for 1 hour and repeats this four more times, that is, 5 upstream and 5 downstream journeys. Then the boat will be

  1. 20 km downstream of A

  2. 15 km downstream of A

  3. 22.5 km downstream of A

  4. 12.5 km downstream of A
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Upstream speed = 96/8 = 12 km/hr. Downstream speed = 96/6 = 16 km/hr. Let boat speed be B and stream speed be S. B-S=12, B+S=16. Adding gives 2B=28, B=14. Subtracting gives 2S=4, S=2. In 1 hour downstream, it goes 16 km. In 1 hour upstream, it goes 12 km. Net displacement per 2-hour cycle = 16 - 12 = 4 km downstream. In 5 cycles (10 hours), total displacement = 5 * 4 = 20 km downstream.

AI explanation

First, we calculate the upstream speed as 96 km divided by 8 hours, which is 12 km/hr, and the downstream speed as 96 km divided by 6 hours, which is 16 km/hr. During each cycle of one hour downstream and one hour upstream, the boat gains a net distance of 16 minus 12, equaling 4 km downstream from point A. Since the boat repeats this cycle five times, the total displacement from point A is 5 multiplied by 4 km. The boat will be 20 km downstream of point A.

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