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    Question

    Each question is followed by three statements I, II and

    III. You have to decide whether the data given in the statements are sufficient to answer the question. What is the speed of Train A in km/h? I. Train A passes a pole in 12 seconds. II. Train A passes a 480 m long platform in 36 seconds. III. Train A crosses another train B of length 160 m, running in the same direction at 36 km/h, in 40 seconds.
    A If the data in statement I alone are sufficient, but the data in statements II and III alone are not sufficient. Correct Answer Incorrect Answer
    B If the data in statement II alone are sufficient, but the data in statements I and III alone are not sufficient. Correct Answer Incorrect Answer
    C If the data in statement III alone are sufficient, but the data in statements I and II alone are not sufficient. Correct Answer Incorrect Answer
    D If the data in any two of the three statements together are sufficient, but no single statement alone is sufficient. Correct Answer Incorrect Answer
    E If the data in all three statements together are necessary to answer the question; even any two statements together are not sufficient. Correct Answer Incorrect Answer

    Solution

    ATQ, Let length of Train A = L metres, speed of Train A = v m/s. Convert 36 km/h of Train B to m/s: 36 × (5/18) = 10 m/s. Statement I: Time to pass a pole = L / v = 12 ⇒ L = 12v One equation, two unknowns ⇒ not sufficient alone. Statement II: Time to pass platform length 480 m: (L + 480)/v = 36 ⇒ L + 480 = 36v …(A) Again one equation, two unknowns ⇒ not sufficient alone. Statement III: Trains in same direction, relative speed = v − 10 m/s. Distance to cover = L + 160. Time = 40 s: (L + 160)/(v − 10) = 40 ⇒ L + 160 = 40(v − 10) = 40v − 400 …(B) Again one equation, two unknowns ⇒ not sufficient alone. Now check any two: I + II: From I: L = 12v Substitute into (A): 12v + 480 = 36v ⇒ 480 = 24v ⇒ v = 20 m/s Convert to km/h: 20 × (18/5) = 72 km/h. Unique speed ⇒ I + II sufficient. I + III: From I: L = 12v Substitute into (B): 12v + 160 = 40v − 400 ⇒ 40v − 12v = 160 + 400 ⇒ 28v = 560 ⇒ v = 20 m/s ⇒ 72 km/h. I + III also sufficient. II + III: From (A): L = 36v − 480 From (B): L = 40v − 560 Equate: 36v − 480 = 40v − 560 ⇒ 40v − 36v = −480 + 560 ⇒ 4v = 80 ⇒ v = 20 m/s ⇒ 72 km/h. II + III also sufficient. Thus: – No single statement alone is sufficient. – Any two statements together are sufficient to find the speed of Train A.

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