Two trains A and B travel in two parallel rain tracks in opposite direction with speed `v_(1)` and `v _(2)` respectively. They take 4 s to pass each other at this speed. If thte speed of train A is increased by `50%` then they take 3 s to pass each other. The ratio of `v_(1)//v_(2)` is

Options

A. `0.5`
B. `1.5`
C. `2.1`
D. `2.5`

Answer

C

Explanation

Relative velocity of trains `= v_(1) + v_(2)` Let distance between them is s.
(i) First they take 4 s to cross
`s = (v_(1) + v _(2)) 4 " "…(i)`
(ii) Second they take 3 s to cross, when speed of train A is increased by `50%`
Now, relative velocity `= (v_(1)+ (50)/(100) v _(1))+ v_(2)= ((3)/(2) v _(1) + v_(2))`
`therefore s = ((3)/(2) v_(1) + v_(2)) 3 " "...(ii)`
From Eqs. (i) and (ii) , we get
`(v_(1) + v_(2)) 4= ((3)/(2) v_(1) + v _(2)) 3 implies v _(2) = (v_(1))/(2) implies (v_(1))/(v_(2)) = 2/1`