Multiple choice

A train $X$ starts from New Delhi at $4$ pm and reaches Ghaziabad at $5$ pm. While another train $Y$ starts from Ghaziabad at $4$ pm and reaches New Delhi at $5 : 30$ pm. At what time will the two trains cross each other?

  1. $4 : 30$ pm
  2. $4 : 24$ pm
  3. $4 : 36$ pm
  4. $4 : 41$ pm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train X speed is 1 unit/hour (distance/1 hr). Train Y speed is 1 unit/1.5 hours = 2/3 units/hour. Relative speed is 1 + 2/3 = 5/3 units/hour. They meet at time t = distance / relative speed = 1 / (5/3) = 3/5 hours. 3/5 hours = 36 minutes. Starting at 4 pm, they cross at 4:36 pm.

AI explanation

Let the distance be D; train X takes 1 hour and train Y takes 1.5 hours, so their speeds are D and 2D/3 per hour. At any time t hours after 4 pm, the total distance covered by both trains must equal D, giving the equation D*t + (2D/3)*t = D. Solving for t yields 5t/3 = 1, so t = 0.6 hours, which is 36 minutes; therefore, they cross at 4:36 pm.

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