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An express train leaves Agra and passenger train leaves Delhi towards each other at same time and continue running between these two cities. Whenever they meet, they exchange their speed and returned. If the initial ratio of speed is 2 ∶ 1. If they meet at Point P for the first time then the ratio of distance covered by express to passenger train till they meet for the second

An express train leaves Agra and passenger train leaves Delhi towards each other at same time and continue running between these two cities. Whenever they meet, they exchange their speed and returned. If the initial ratio of speed is 2 ∶ 1. If they meet at Point P for the first time then the ratio of distance covered by express to passenger train till they meet for the second Correct Answer 4 : 5

Let the distance between the stations be 3x km and the speed of the express train and passenger train be 2x km/h and x km/h respectively and

We know that

Speed = Distance/Time

⇒ Time of first meeting = 3x/(2x + x) = 1 hr

Distance covered by Express train till first meeting = 2x km

Distance covered by Passenger train till first meeting = x km

⇒ Time taken by Express train to reach Delhi after meeting = (3x – 2x)/x = 1 hr

⇒ Time taken by Passenger train to reach Agra after meeting = (3x – x)/2x = 1 hr

Time of second meeting = 3x/(2x + x) = 1 hr

Distance covered by Passenger train after first meeting = 2x × 2 = 4x km

Distance covered by Express train after first meeting = x × 2 = 2x km

∴ Required ratio = (2x + 2x) : (x + 4x) = 4 : 5

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