Each question below contains a statement followed by Quantity I and Quantity
II. Compare the value derived from Quantity I and Quantity II and choose the correct option. A train crosses a pole in 15 seconds and crosses a platform of length 250 meters in 30 seconds. Which of the following options correctly represents the relationship between Quantity I and Quantity II? Quantity I: Speed of the train (in km/h). Quantity II: 65 km/h.

Let the length of the train be L meters and its speed be S m/s. ATQ, the train crosses a pole in 15 seconds. So, L = S × 15 = 15S ... (i) Also, the train crosses a platform of length 250 meters in 30 seconds. So, L + 250 = S × 30 = 30S ... (ii) Substituting (i) in (ii): Or, 15S + 250 = 30S Or, 30S - 15S = 250 Or, 15S = 250 Or, S = 250 / 15 = 50/3 m/s Now, converting speed into km/h: Or, Speed = 50/3 × 18/5 = 10 × 6 = 60 km/h Thus, Quantity I = 60 km/h and Quantity II = 65 km/h. Therefore, Quantity I < Quantity II. Hence, the correct answer is B.