Multiple choice

A man is standing between the two parallel tracks. A passenger train reduces its speed in order to stop. The speed of the passenger train is 18 km/hr. It takes 30 seconds for the train to pass the man. Another train carrying goods doesn't stop and crosses the man in 4 seconds. The two trains cross each other in 8 seconds. Which of the following can be obtained from the above given information? (i) Time taken by the train which is carrying goods to cover the distance four times its length (ii) Time taken by the car to cross the man if the speed of the car is doubled (iii) Speed of the train carrying goods (iv) Ratio of the speed of the passenger train to that of the train carrying goods

  1. (i) only

  2. (i) and (iv) only

  3. (i), (iii) and (iv)

  4. (i) and (iii) only

  5. All (i), (ii), (iii) and (iv)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The passenger train length is 5 × 30 = 150 m. If the goods train speed is v m/s, its length is 4v, and crossing both trains in 8 seconds gives 150 + 4v = 8(5 + v), so v = 27.5 m/s. Thus statements (i), (iii), and (iv) can be obtained, while (ii) refers to an undefined car.

AI explanation

The passenger train travels at 5 meters per second, so its length is 5 multiplied by 30, which equals 150 meters. If the goods train crosses the man in 4 seconds, its length is 4g where g is its speed; because they cross each other in 8 seconds, 150 plus 4g equals 8 multiplied by the sum of 5 and g, which solves to g equaling 45 meters per second. This allows calculation of the speed and the ratio of speeds, and the time to cover four times its length is 16 seconds; the speed of the car cannot be found. The items (i), (iii) and (iv) can be obtained.

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