Multiple choice

Swati can row a boat in still water at a speed of 5 km/hr. However, in a given river, it takes her 1 hour more to row the boat 12 km upstream than downstream. One day, Swati rows the boat in this river from X to Y, which is N km upstream from X. Then she rows back to X immediately. If she takes at least 2 hours to complete this round trip, what is the minimum possible value of N?

  1. 2

  2. 2.1

  3. 4.8

  4. 3.6

  5. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed of stream be v. Upstream speed = 5-v, downstream = 5+v. Time difference: 12/(5-v) - 12/(5+v) = 1. Solving gives v=1. Round trip time for distance N: N/(5-v) + N/(5+v) = N/4 + N/6 = 5N/12. We need 5N/12 >= 2, so N >= 24/5 = 4.8.

AI explanation

Using the given information for 12 km, the upstream speed is 5 minus y and the downstream speed is 5 plus y, so 12 divided by 5 minus y minus 12 divided by 5 plus y equals 1; solving this gives the stream speed y as 1 km/hr. For the round trip of N km to take at least 2 hours, the time equation is N divided by 4 plus N divided by 6 is greater than or equal to 2. Solving this inequality gives N is greater than or equal to 4.8, making the minimum possible value 4.8.

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