`A` and `B` are two fixed spots in a river in which water has a steady sped `v_(w)`. A person who can swim with a speed `v` relative to water swims from `A` to `B` and back to `A` alomg shortest path. If the

water is still, the person will take a time `30` minute in swimming from `A` to `B` and back to `A` along the shortes path. But we know that water is acually not still. The person also knows the technique of just flowing with water without exerting his own effort. Using this technique, i.e., just being carried with water, he takes a time `20` minute in moving from `A` to `B`. As shown, `X` and `Y` are two places directly oppsite to each other on oppsite banks. Assuming that width of the river is the same as the distance `A` and `B`, answer these questions. (assume `v gt v_(w)`)
Choose the correct option(s) :

Options

A. Time taken by the person to swim from `B` to `A` (in running water) is `60` min
B. Time taken by the person to swim from `B` to `A` (in running water) is `45` min
C. Time taken by the person to swim from `B` to `A` (in running water) is `(60)/(7)` min
D. Time taken by the person to swim from `B` to `A` (in running water) is `10` min

Answer

A, C

Explanation

Let `L =` distance `A` and `B` which is also equal to that between `X` and `Y`
From `A` and `B` back to `A`
`2L = V 30`
`V = L/15`, When river flowing then from A to B
`V_(W) = (L)/(20)`
Time from `B` to `A = (L)/(V - V_(W)) = (L)/((L)/(15) - (L)/(20)) = 60` min.