Problem 12

Explanation

An analog clock (12-hour format) will show the same time as a normal clock again when the time difference reaches a multiple of 12 hours.

Converting Units to Minutes

Since the delay is given in minutes, we convert 12 hours into minutes:

Calculating the Required Time

It is known that the clock loses $5$ minutes every hour. We want to find how many hours ($n$) it takes for the total delay to reach $720$ minutes.

Thus, the clock will show the same time as a normal clock after 144 hours.