Multiple choice

Passage

Directions: Read the following information and answer the given question. Trains A and B run between stations P, Q and R. These stations are in the same line, station Q being between stations P and R. The total distance between stations P and R is 300 km. The ratio of the distance between stations P and Q to that between stations Q and R is 3 : 2. Train A starts from station P and train B starts from station Q, and both travel towards station R.

On one day, both trains A and B start at the same time; their speeds are 5t km/hr and 4t km/hr, respectively. Train A goes non-stop till station R, while train B stops in between for 2t minutes before reaching station R. If both trains reach R at the same time, then what is the value of t?

  1. 15

  2. 30

  3. 45

  4. 60
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

PQ:QR = 3:2. Total 300km, so PQ = 180km, QR = 120km. Train A (P to R) = 300km at 5t km/hr. Time = 300/(5t) = 60/t hours. Train B (Q to R) = 120km at 4t km/hr. Time = 120/(4t) + (2t/60) hours. 60/t = 30/t + t/30. 30/t = t/30, so t^2 = 900, t = 30.

AI explanation

The total distance between stations P and R is 300 km, and the ratio of distances 3:2 means station R is 120 km from station Q. The travel time for train A to reach R is 300 / (5t) hours, or 60/t hours, and the total time for train B is its travel time of 120 / (4t) plus its stoppage time, which is 2t/60 hours. Setting their times equal gives 60/t = 30/t + t/30; solving this equation results in t = 30.

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