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GATE 2025 CE (CE1) – Question 7

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

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?

  1. $64\frac{6}{11}$
  2. $66\frac{5}{13}$
  3. $65\frac{5}{11}$
  4. $66\frac{6}{13}$

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Correct answer: (C) $65\frac{5}{11}$

Explanation

The minute hand gains $5.5^\circ$ per minute on the hour hand, because it moves $6^\circ$ per minute and the hour hand $0.5^\circ$ per minute. The hands coincide again after it has gained $360^\circ$, which takes $\frac{360}{5.5} = \frac{720}{11} = 65\frac{5}{11}$ minutes.