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.

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.