Multiple choice

A train $M$ leaves Meerut at $5$ $a.m.$ and reaches Delhi at $9$ $a.m.$ Another train $N$ leaves Delhi at $7$ $a.m.$ and reaches Meerut at $10.30$ $a.m.$ At what time does the two trains cross each other?

  1. $7.36$ $a.m.$
  2. $7.56$ $a.m.$
  3. $8$ $a.m.$
  4. $8.26$ $a.m.$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train M speed = D/4. Train N speed = D/3.5. M starts at 5, N at 7. By 7 am, M has traveled 2 hours = D/2. Distance between them at 7 am = D/2. Relative speed = D/4 + D/3.5 = (3.5+4)D/14 = 7.5D/14. Time = (D/2) / (7.5D/14) = 7/7.5 = 14/15 hours = 56 minutes. 7 am + 56 min = 7:56 am.

AI explanation

Let the total distance be D. Train M takes 4 hours, so its speed is D/4. Train N takes 3.5 hours, so its speed is D/3.5, or 2D/7. By 7 a.m., train M has traveled for 2 hours, covering a distance of 2D/4, leaving a remaining distance of D/2. Using the relative speed formula for objects moving towards each other, their relative speed is D/4 + 2D/7 = 15D/28. The time taken to meet is the remaining distance divided by the relative speed: (D/2) divided by (15D/28) equals 14/15 hours, or 56 minutes. Adding this to 7 a.m. gives a crossing time of 7.56 a.m.

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