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Question

Consider the following for the next three (03) items that follow:
Two trains A and B started from stations P and Q respectively towards each other. Train A started at 7 p.m. at a speed of 60 km/hr and train B started at 4 a.m. (next day) at a speed of 90 km/hr. The distance between the two stations P and Q is 800 km.

At what time will the two trains meet?

This question was previously asked in
CDS 2 2024 Maths Question Paper (01-Sep-2024)
The correct answer is
5:44 a.m.

To find the time when the two trains meet, we need to calculate when the distance covered by both trains together equals the total distance between the two stations.

Let us break down the problem step-by-step:

  1. Train A starts at 7 p.m. from station P and travels at a speed of 60 km/hr.
  2. Train B starts at 4 a.m. the next day from station Q and travels at a speed of 90 km/hr.
  3. The total distance between stations P and Q is 800 km.

First, we need to determine how far Train A travels before Train B starts:

  • Time from 7 p.m. to 4 a.m. is 9 hours.
  • Distance covered by Train A in 9 hours \(= 60 \, \text{km/hr} \times 9 \, \text{hours} = 540 \, \text{km}\).

Now, calculate the remaining distance that they need to cover before meeting:

  • Remaining distance \(= 800 \, \text{km} - 540 \, \text{km} = 260 \, \text{km}\).

Next, determine the relative speed of both trains when they move towards each other:

  • Relative speed \(= 60 \, \text{km/hr} + 90 \, \text{km/hr} = 150 \, \text{km/hr}\).

Calculate the time taken to cover the remaining distance:

  • Time taken \(= \frac{260 \, \text{km}}{150 \, \text{km/hr}} = \frac{26}{15} \, \text{hours} = 1.7333 \, \text{hours}\).
  • Convert hours to minutes: \(1 \, \text{hour} = 60 \, \text{minutes}\)
  • So, \(0.7333 \, \text{hours} = 0.7333 \times 60 \approx 44 \, \text{minutes}\).

Finally, add this time to the 4 a.m. starting time of Train B:

  • Time when trains meet \(= 4:00 \, \text{a.m.} + 1 \, \text{hour} \, 44 \, \text{minutes} = 5:44 \, \text{a.m.}\).

Thus, the correct answer is 5:44 a.m..

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Similar Questions

  1. Train \(X\) crosses a man standing on the platform in 24 seconds and train \(Y\) crosses a man standing on the platform in 18 seconds. They cross each other while running in opposite directions in 20 seconds. What is the ratio of speed of \(X\) to speed of \(Y\)?

  2. How far from station Q will the two trains meet?
     

  3. If the lengths of the two trains A and B are 400 m and 500 m respectively, then what is the time taken by them to cross each other?
     


Important Questions from Problem on Trains

  1. Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.

    If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?

  2. A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service?

  3. A train with a uniform speed passes a 122 meters long platform in 17 seconds and a 210 meters long bridge in 25 seconds. The speed of the train is:

  4. How long does a train 153 meters long running at the rate of 90 kmph take to cross a bridge 622 meters in length?

  5. A train passes a 360 metre long platform in 40 seconds and a man standing on the platform in 16 seconds. The speed of the train is:

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