Discussion
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?
Answer: C
Rohit spent \(65\frac{5}{11}\) minutes at the restaurant.
The minute hand moves 6° per minute and the hour hand 0.5° per minute, so the minute hand gains 5.5° per minute. To coincide again it must gain a full 360°:
\[ \begin{aligned} t &= \frac{360}{5.5} = \frac{720}{11} \\ &= 65\frac{5}{11}\ \text{min} \end{aligned} \]
He arrived when the hands met just after 1 o'clock (at about 1:05) and left when they next met (at about 2:11), so the time between is one full coincidence interval.
The other mixed numbers do not equal 720/11; the ones with 13 in the denominator are not based on the hands' relative speed at all.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development