Two trains take `3s` to pass another when going in the opposite directions but only `2.5s` if the speed of one is increased by `50%`. The time one would take to pass the other when going in the same direcrtioin at their original speed is

Options

A. `10` sec.
B. `12` sec.
C. `15` sec.
D. `18` sec.

Answer

C

Explanation

`t_(1)=3=(2L)/(v_(1)+v_(2))impliesv_(1)+v_(2)=(2L)/(3)` ….(i)
`{:(t_(2)=2.5=(2L)/(1.5v_(1)+v_(2)),1.5v_(1)+v_(2)=(4L)/(5)):}` ……. (ii)
by (i) and (ii)
`v_(1)=(4L)/(15):v_(2)=(2L)/(5)`
Now, `t_(3)=(2L)/(|v_(1)-v_(2)|)=(2L)/(2L//15)=15` sec.