Question

A clock loses 1 second every minute. It is set to the correct time at 10 AM on February 4. In which month is the next day on which it shows the correct time? (Note: A person can see whether it is AM or PM on this clock.)

Answer 1

Answer: The month of April

More accurately: The correct time will be shown on April 4th if it is a leapyear, or April 5th if it is a non-leapyear. It takes 60 days for the clock to realign, which is the same as saying "the clock loses 24 hours every 60 days".

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Explanation:

The following statements shown below are all equivalent to one another.

• Clock loses 1 second every 1 minute (original statement)
• Clock loses 60 seconds every 60 minutes (multiply both parts of previous statement by 60)
• Clock loses 1 minute every 1 hour (time conversion)
• Clock loses 60 minutes every 60 hours (multiply both parts of previous statement by 60)
• Clock loses 1 hour every 2.5 days (time conversion)
• Clock loses 24 hours every 60 days (multiply both parts of previous statement by 24)

Use a Day-Of-Year calendar to quickly jump ahead 60 days into the future from Feb 4th (note how Feb 4th is day 35; add 60 to this to get to the proper date in the future). On a leapyear (such as this year 2020), you should land on April 4th. On a non-leapyear, you should land on April 5th. The extra day is because we lost Feb 29th.

The actual day in April does not matter as all we care about is the month itself only. Though it's still handy to know the most accurate length of time in which the clock realigns itself.