Multiple choice

Train 𝑋 travels from Howrah to Prayagraj whereas train π‘Œ travels from Prayagraj to Howrah. Trains 𝑋 and π‘Œ leave Howrah and Prayagraj on Sunday at 5 AM and 8 AM, respectively. The trains travel on parallel track and cross each other at 20 minutes past 1 PM on the same day. If both the trains reach their destinations simultaneously at a certain time 𝑑, then 𝑑 must be

  1. 7:20 PM on Sunday

  2. 7:50 PM on Sunday

  3. 9:20 PM on Sunday

  4. 8:00 PM on Sunday
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the distance be D. Train X speed = D/T1, Train Y speed = D/T2. They meet at 1:20 PM. Train X traveled from 5 AM to 1:20 PM (8 hours 20 mins = 25/3 hours). Train Y traveled from 8 AM to 1:20 PM (5 hours 20 mins = 16/3 hours). Distance covered by X + Y = D. (D/T1)(25/3) + (D/T2)(16/3) = D. 25/3T1 + 16/3T2 = 1. If they arrive simultaneously at time t, they travel for times (t-5) and (t-8). Solving for t leads to 8:00 PM.

AI explanation

Let the speeds of train X and Y be Sx and Sy. They cross each other at 1:20 PM, meaning train X travelled for 8.33 hours (25/3 hours) while train Y travelled for 5.33 hours (16/3 hours), so the total distance is Sx times 25/3 plus Sy times 16/3. Since they reach their destinations at the same time, the remaining distance for train X is covered by Y in that time, and the remaining distance for Y is covered by X. This means the time taken by train Y to reach Howrah equals the time taken by train X to reach Prayagraj, which implies (Sx times 16/3) divided by Sy equals (Sy times 25/3) divided by Sx. Solving this gives the ratio Sx to Sy as 5 to 4. The total time taken by train X to complete the journey is its travel time to the crossing point plus the remaining time. The remaining time is the distance covered by train Y divided by the speed of train X, which calculates to 6 hours and 40 minutes. Adding this to the crossing time of 1:20 PM gives a final arrival time of 8:00 PM.

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