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A train $\text{X}$ departs from station $\text{A}$ at $11.00$ a.m. for station $\text{B},$ which is $180$ km away. Another train $\text{Y}$ departs from station $\text{B}$ at $11.00$ a.m. for station $\text{A}$. Train $\text{X}$ travels at an average speed of $70$ km/hr and does not stop anywhere until it arrives at station $\text{B}$. Train $\text{Y}$ travels at an average speed of $50$ km/hr, but has to stop for $15$ minutes at station $C$, which is $60$ km away from station $\text{B}$ enroute to station $\text{A}$. Ignoring the lengths of the trains, what is the distance, to the nearest km, from station $\text{A}$ to point where the trains cross other?

  1. $112$
  2. $118$
  3. $120$
  4. None of these
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