Two swimmers start a race. One who reaches the point `C` first on the other bank wins the race.`A` makes his strokes in a direction of `37^(0)` to the river flow with velocity `5km//hr` relative to water. `B` makes his strokes in a direction `127^(0)` to the river flow with same relative velocity.River is flowing with speed of `2km//hr` and is `100m` wide.speeds of `A` and `B` on the ground are `8km//hr` and `6km//hr` respectively.

Options

A. `A` will win the race
B. `B` will win the race
C. the time taken by `A` to reach the point `C` is `165 sec`
D. the time taken by `B` to reach the point `C` is `150 sec`

Answer

A, D

Explanation

time to cross river `=100/(5xxsin 37xx5/18)=120 sec`
Drift covered `=(2+5xxcos 37)xx5/18xx120=200`
Distance covered by walk `=100` meters and time taken `=20` seconds And similarly for swimmer `B`