Question
The speeds of two trains, P and
Q, are in the ratio of 4:5. The length of train P is 300 meters. What is the speed of train Q? Statement I: Trains P and Q can cross each other in 20 seconds when they are moving in opposite directions. Statement II: Train P can cross a dog running in the opposite direction at a speed of 10 km/h in 20 seconds. The question consists of two statements numbered "l and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.Solution
ATQ, Let the speed of trains ‘P’ and ‘Q’ be 4x km/hr and 5x km/hr, respectively Statement I: According to the question, Let the length of train ‘Q’ be ‘l’ metres (4x + 5x) × (5/18) = (300 + l)/20 Or, 100x = 600 + 2l So, data in statement I alone is not sufficient to answer the question. Statement II: (4x + 10) × (5/18) = 300/20 Or, 20x + 50 = 18 × 15 = 270 Or, 20x = 220 Or, x = 11 Therefore, speed of train ‘Q’ = 5x = 55 km/hr So, data in statement II alone is sufficient to answer the question. So, data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
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