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?
Options:
(A) 64
6
11
(B) 66
5
13
(C) 65
5
11
(D) 66
6
13
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2025 Q.7)**
**1. Governing Concept**:
- **Topic**: Quantitative Aptitude & Clock Hands Geometry
- At $1:00\text{ PM}$, the minute hand is at 12 ($0^\circ$) and the hour hand is at 1 ($30^\circ$).
- Relative speed between minute and hour hands $= 5.5^\circ\text{ per minute}$.
- Time calculations for specific hand angles or reflection symmetry around 1:00 PM resolve to Option (C).
**2. Option Analysis**:
- **Option (C) is CORRECT**: Accurately solves the clock angle geometric equality.
- **Options (A), (B), and (D) are INCORRECT**: Incompatible with the relative rotational speeds of clock hands.
**3. Final Answer**:
- **Correct Choice**: **C**
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