Rohit goes to a restaurant for lunch at about 1 PM. When he enters the…
2025
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. \(65\frac{5}{11}\) — The hands coincide whenever the minute hand has gained one full revolution on the hour hand. The minute hand gains at \(6^\circ/\text{min}\) and the hour hand…
- A.
\(64\frac{11}{65}\)
- B.
\(66\frac{5}{11}\)
- C.
\(65\frac{5}{11}\)
- D.
\(66\frac{6}{13}\)
Show answer & explanation
Correct answer: C
The hands coincide whenever the minute hand has gained one full revolution on the hour hand. The minute hand gains at \(6^\circ/\text{min}\) and the hour hand at \(0.5^\circ/\text{min}\), so the relative gain is \(5.5^\circ/\text{min}=\frac{11}{2}^\circ/\text{min}\). Thus the interval between coincidences is \(\frac{360}{\frac{11}{2}}=\frac{720}{11}=65\frac{5}{11}\) minutes. Since Rohit enters at a coincidence and leaves at the next one after about an hour, he spends \(65\frac{5}{11}\) minutes.