Question

Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are exactly coinciding. After about an hour, when he leaves the restaurant, he notices that the clock hands are again exactly coinciding. How much time (in minutes) did Rohit spend at the restaurant?

• A. \(64 \frac{6}{11}\) minutes
• B. \(66 \frac{5}{13}\) minutes
• C. \(65 \frac{5}{11}\) minutes
• D. \(66 \frac{6}{13}\) minutes

Hint:

Understanding the mechanics of clock hands can help solve problems involving time calculations. The hands coincide 11 times in every 12-hour period.

Answer 1

The Correct Option is C

Step 1: Calculate the frequency of coinciding hands.
The hands of a clock coincide approximately every 65.45 minutes. 
Step 2: Determine the time Rohit spent at the restaurant.
Given that the clock hands coincide approximately every 65.45 minutes and Rohit noticed them coinciding around 1 PM (typically when they would coincide shortly after the hour), the next coincidence would be slightly over 65 minutes. 
Thus, \(65 \frac{5}{11}\) minutes, as an approximation, fits perfectly with our expectation based on the clock's behavior.