Multiple choice

Ram, Shyam and Hari went out for a 100 km journey. Ram and Hari started the journey in Ram's car at the rate of 25 kmph, while Shyam walked at 5 kmph. After some time, Hari got off and started walking at the rate of 5 kmph and Ram went back to pick up Shyam. All three reached the destination simultaneously. The number of hours required for the trip was

  1. 8 hours

  2. 7 hours

  3. 6 hours

  4. 5 hours

  5. 4 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let t be the total time. Ram travels 25t total distance. Shyam walks 5t. The logic of the trip implies they all arrive at the same time, and solving the relative motion equations gives 8 hours.

AI explanation

By setting the total distance to 100 km and the walking speed at 5 kmph and car speed at 25 kmph, we can equate the total travel time for Shyam and Hari. Hari walks for a distance D and rides for (100 - D), taking D/5 + (100 - D)/25 hours, while Shyam walks for distance d and rides for (100 - d), taking d/5 + (100 - d)/25 hours. Because Ram drives for the exact same amount of time that the passengers are in the car to balance the forward and backward trips to drop and pick them up, solving the time equations yields a total journey time of 8 hours for everyone.

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