Taxies leave station `X` for station `Y` every `10 min`. Simultaneously, a taxi also leaves station `Y` for station `X` every `10 min`. The taxies move at the same constant speed and go from `X` and `Y` or vice-versa in `2 h`, How many taxies coming from the other side will meet each taxi enroute from `Y` and `X`?.

Options

A. `24`
B. ` 23`
C. ` 12`
D. ` 11`

Answer

B

Explanation

Because one taxi leaces very `10 min`, at any instant there will be `11` taxies on the way towards each station, on will be arriving and another leaving the other station. Figure shows the locatopm of taxies going from `X` to `Y` at the instant `2.00 PM`.The taxi which leaves station `X` at `0.00 PM` has just arrived at the station `Y`. Consider the taxi leaving the station `Y` at `2.00 PM`.
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I will meet all the `11` taxies marked `1` to `11` as well as `12` other taxies which would leave the station `X` from `2.00 PM` to `3.50 PM`. When it arrives at the station `X` at `4.00 PM`, there will be on more taxi leaving that station. However, it will not be counted among the taxies crossed by taxi under consideration. That is , it will cross `23` taxies leaving the station `X` from `(0)/(10) PM` to `3.50 PM`.