# Digital Clock

• Feb 10th 2007, 09:44 AM
aznmartinjai
Digital Clock
A digital clock displays the time along with the a.m and p.m. abbreviation. The clock shows the correct time on January 1, 2006, at noob. If the clock loses 15 minutes per day, what will be the next date when the clock displays the correct time and abbreviation (a.m./p.m.)?
• Feb 10th 2007, 11:59 AM
ticbol
Quote:

Originally Posted by aznmartinjai
A digital clock displays the time along with the a.m and p.m. abbreviation. The clock shows the correct time on January 1, 2006, at noob. If the clock loses 15 minutes per day, what will be the next date when the clock displays the correct time and abbreviation (a.m./p.m.)?

There was a similar problem to this that I've done here before.

So after one day, the clocks time is 15 minutes less.
Correct time = 12:00 Noon, clock's time = 11:45 AM......Jan 2

After 2 days,
Correct time = 12:00 Noon, clock's time = 11:30 AM......Jan 3

After 4 days,
Correct time = 12:00 Noon, clock's time = 11:00 AM......Jan 5

So in 4 days there is a loss/delay of 1 hour.

Hence, for a 24-hr loss/delay, there will be 24*4 = 96 days to pass after the noon of January 1.

Since there are 24 hours between the first showing of the "AM" in the clock and the next showing after the many "PM's"---imagine 12:01 AM to 12:01 AM again---then the next 12:01 PM to be shown on the erroneous clock will be after 96 days from the 12:01 PM of January 1.

So if not leap year, or February has 28 days only,

31 days of January
28 days of February
31 days of March
-----------
90 days sub-total

6 days more.
So, April 6.

Therefore, if not leap year, the clock will display again the correct time and abbreviation on April 6, 12:01 PM. -------------answer.
• Feb 11th 2007, 06:18 AM
aznmartinjai
Thanks you so much Ticbol ;D