Clock angle change — What is the percentage change in the (smaller) angle between the minute and hour hands from 2:00 PM to 6:00 PM?

Introduction / Context:
We compare the smaller inter-hand angle at two specified times and compute the percentage increase.

Given Data / Assumptions:

• At 2:00, hour angle = 60°, minute angle = 0° → smaller angle = 60°.
• At 6:00, hour angle = 180°, minute angle = 0° → smaller angle = 180°.

Concept / Approach:
Percentage change = ((new − old)/old) * 100.

Step-by-Step Solution:
Old (2:00) = 60°.New (6:00) = 180°.Increase = 180 − 60 = 120°.Percentage change = (120/60)*100 = 200%.

Verification / Alternative check:
Graphing the smaller angle across hours shows it attains 180° at 6:00, confirming the calculation.

Why Other Options Are Wrong:
100%/250% do not match the exact computation; “None” is wrong because 200% is valid.

Common Pitfalls:
Using the reflex angle at 6:00 (also 180° here, but conceptually some problems request the smaller angle—identical here).

Final Answer:
200 (percent).