Multiple choice

Directions : Answer the question independently. Radha walks at a constant speed on a road parallel to the railway track joining Rampur and Laxmanpur stations in the direction towards Laxmanpur. Trains shuttle between the two stations throughout the day. Trains start from either station at the same time with same speed (which remains constant throughout the journey). The time between the consecutive trains starting from either station is also same. She observes that the train from Rampur to Laxmanpur crosses her after every 12 minutes while the train from Laxmanpur crosses her after every 8 minutes. What is the time interval between the two consecutive trains travelling in either direction?

  1. 48/5 min

  2. 48/7 min

  3. 34/5 min

  4. 23/7 min

  5. Culture influences choice making. Individualistic societies are taught the importance of personal choice while collectivist societies emphasize that what you eat, what you play with, what you study etc should be determined by society and should not be left to the whims of the individual.
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A Correct answer
Explanation

Let the interval between departures from the same station be T. Relative-speed relations for trains moving with and against Radha give T = 24/5 minutes. The interval between consecutive trains travelling in either direction is twice this value, 48/5 minutes.

AI explanation

Let S be the train speed, W be Radha's walking speed, and T be the interval between trains. The distance between trains is S times T, so the meeting frequency for oncoming trains is S plus W divided by S times T equals 1 over 8, and for trains from behind it is S minus W divided by S times T equals 1 over 12. Adding these two equations eliminates W, yielding 2S divided by S times T equals 1 over 8 plus 1 over 12. Solving this gives 2 over T equals 5 over 24, which means T is 48 divided by 5 minutes.

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