A swimmer crosses a river with minimum possible time 10 Second. And when he reaches the other end starts swimming in the direction towards the point from where he started swimming. Keeping the direction fixed the swimmer crosses the river in 15 sec. The ratio of speed of swimmer with respect to water and the speed of river flow is (Assume contant speed of river & swimmer)

Options

A. `3/2`
B. `9/4`
C. `(2)/(sqrt5)`
D. `(sqrt5)/2`

Answer

C

Explanation

V = velocity of man w.r.t., river
u = velocity of river
`A overset(t)(rarr)B = d/v implies 10 = d/v`
`implies d = 10 V rarr (1)`
`Boverset(t)(rarr)C = d/(v cos theta) implies 15 = d/(v cos theta)`
`implies d = 15v cos theta rarr (2)`
(1) & (2) `implies cos theta = 2//3 implies "sec" theta = 3//2`
`:' tan theta = u/v`
`:. sqrt("sec"^(2)theta -1) = u/v`
`implies u/v = sqrt(9//4 -1) = (sqrt5)/(2) implies v/u = 2/(sqrt5)` .