Multiple choice

Passage

Directions: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You are to use the given data and your knowledge of Mathematics to choose among the given options.

Quantity I: A train running at a speed of 90 km/hr crosses a 0.18 km long platform in half a minute. Time taken by it to cross a 280 m long platform Quantity II: A 300 m long train crosses a still car in half a minute. Time taken by it to cross another car with a speed of 18 km/hr travelling in the opposite direction (Assuming the length of the car negligible w.r.t. the train)

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I = Quantity II or no relation can be established.

  5. Quantity I ≤ Quantity II
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Speed = 90 km/hr = 25 m/s. Time to cross 0.18 km (180 m) platform: (Length of train + 180) / 25 = 30. Length of train = 750 - 180 = 570 m. Time to cross 280 m platform: (570 + 280) / 25 = 850 / 25 = 34 seconds. Quantity II: 300 m train crosses car in 30s. Speed of train = 300 / 30 = 10 m/s. Relative speed with car at 18 km/hr (5 m/s) in opposite direction = 10 + 5 = 15 m/s. Time = 300 / 15 = 20 seconds. 34 > 20.

AI explanation

Convert the speed to 25 meters per second for Quantity I, where the total crossing distance in 30 seconds is 750 meters, making the train length 570 meters; the time to cross a 280-meter platform is 850 divided by 25, which equals 34 seconds. For Quantity II, crossing a still car takes 30 seconds, meaning the speed is 10 meters per second; the relative speed with an oncoming car at 5 meters per second is 15 meters per second, making the crossing time 300 divided by 15, which equals 20 seconds. Since 34 seconds is greater than 20 seconds, Quantity I is greater than Quantity II.

Keep practicing — related questions