Question
You’re given three statements (I, II, and III). Based
on the information provided in them, determine whether it’s possible to answer the question: The speed of train X is 90 km/h, and its length is 75% of the length of train Y. What is the length of train Y (in meters)? Statement I:- Rohit runs toward train X at 22.5 km/h, and train X crosses him in 12 seconds. Statement II:- Train X passes a platform whose length is two-fifths of its own in 21 seconds. Statement III:- Trains X and Y, traveling in opposite directions, cross each other in 2 minutes and 55 seconds.Solution
ATQ, Statement I: Speed of Rohit = 22.5 km/h = 22.5 × 5/18 = 6.25 m/s Speed of Train X = 90 km/h = 90 × 5/18 = 25 m/s Since both are moving in opposite directions, relative speed = 25 + 6.25 = 31.25 m/s Length of Train X = 31.25 × 12 = 375 meters Length of Train Y = 375 × (100/75) = 375 X (4/3) = 500 meters So, data in statement I alone is sufficient to answer the question. Statement II: Let the length of Train X = 'm' meters Platform length = (2/5) × m = 0.4m meter Speed of Train X = 90 km/h = 25 m/s ATP, m + 0.4m = 25 × 21 1.4m = 525 m = 525 ÷ 1.4 = 375 meters So, length of Train X = 375 meters So, length of Train Y = 375 × (4 / 3) = 500 meters So, data in statement II alone is sufficient to answer the question. Statement III: Let the length of Train Y = 4m meters Then length of Train X = 3m meters Time taken to cross each other = 2 minutes and 55 seconds = 175 seconds Speed of Train X = 90 km/h = 25 m/s Let the speed of Train Y = ‘s’ m/s Relative speed = (s + 25) m/s Total length = 4m + 3m = 7m So, 7m = (s + 25) × 175 m = (175s + 4375) /7 This gives us a relation between ‘m’ and ‘s’, but not an exact value. So, we cannot determine the exact length of Train Y. So, data in statement III alone is not sufficient to answer the question.
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