How many revolutions does a cycle wheel make in travelling one km? I. It is…

Concept: To find how many times a wheel revolves in covering a distance, you need Revolutions = Distance ÷ Circumference = Distance ÷ (π × Diameter). This depends only on the wheel's size — not on its speed or the time taken. In a data-sufficiency question, a statement is sufficient only if, together with the stem, it lets you compute a single, definite value for what is asked.

Application: Here the stem already fixes the distance (1 km), so what is missing is the wheel's size.

1. Statement I gives the speed (3 km/hour). Speed connects distance and time, not distance and size — so it cannot reveal the circumference. Revolutions therefore cannot be found from statement I alone.

2. Statement II gives the height of the topmost point of the wheel above the ground as 1.3 metres. Since the wheel touches the ground and the top point is diametrically opposite the contact point, this height equals the wheel's diameter — so diameter = 1.3 metres.

3. Circumference = π × diameter = π × 1.3 ≈ 4.08 metres.

4. Revolutions = Distance ÷ Circumference = 1000 metres ÷ 4.08 metres ≈ 245 — a single definite value, computable from statement II alone.

Cross-check: The same result follows using the radius: radius = 0.65 metres, circumference = 2 × π × radius = 2 × π × 0.65 ≈ 4.08 metres — consistent. No information about speed or time was needed anywhere in this computation, confirming statement I is genuinely irrelevant to the revolution count.

So statement II alone is sufficient, while statement I alone is not sufficient.