Right angles per day: How often are the hands of a clock at right angles in a 24-hour day?

Introduction / Context:In every 12-hour cycle, the hands form right angles 22 times (twice per roughly each hour, except around 2–4 hours where spacing shifts). Therefore, over 24 hours the count doubles to 44.

Given Data / Assumptions:

• Standard 12-hour analog clock.
• Uniform motion.

Concept / Approach:Use the known count per 12 h and multiply by 2 for a full day.

Step-by-Step Solution:

Verification / Alternative check:Between consecutive hours there are typically two right-angle instants; summing carefully over 12 hours yields 22.

Why Other Options Are Wrong:38/40/48 miscount the standard total.

Common Pitfalls:Assuming a fixed “two per hour” without accounting for boundary overlaps; the known total 22 per 12 h is robust.

Final Answer:44 times