A conference room has two analog (12-hour format) clocks,

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A conference room has two analog (12-hour format) clocks, one on the north wall and one on the south wall. The clock on the north wall loses 30 seconds per hour, and the clock on the south wall gains 15 seconds per hour. If the clocks begin displaying the same time, after how long will they next display the same time again?

A. 32 days
B. 36 days
C. 40 days
D. 44 days
E. 48 days

We can see that the clock on the north wall loses twice as much time as the clock on the south wall gains. We can assume the time that both clocks display is 12 o’clock, i.e., the hour hand is on the number 12 on both clocks. The next time they will display the same time is 4 o’clock, since the clock on the south wall gains 4 hours and the clock on the north wall loses 8 hours.

From the south clock point of view:

Since 4 hours = 4 x 3600 = 14400 seconds and the clock on the south wall gains 15 seconds per hour, it needs 14400/15 = 960 hours or 40 days to strike 4 o’clock as the clock on the north wall strikes the same time.

Or, from the north clock point of view:

Since 8 hours = 8 x 3600 = 28800 seconds and the clock on the north wall loses 30 seconds per hour, it needs 28800/30 = 960 hours or 40 days to strike 4 o’clock as the clock on the south wall strikes the same time.

In either case, the number of days needed is 40.

Answer: C

Hi All,

We're told that a conference room has two analog (12-hour format) clocks, one on the north wall and one on the south wall; the clock on the north wall LOSES 30 seconds per HOUR, and the clock on the south wall GAINS 15 seconds per HOUR. We're asked, if the clocks begin displaying the SAME time, after how long will they next display the SAME time again. This question can be approached in a number of different way, but you can take advantage of the 'format' of the answer choices to do some minimal math to find the correct answer.

Since all five answers are in 'days', we can think of all of these calculations in terms of how the rates are calculated per day.
The North clock loses 30 seconds/hour; with 24 hours/day, that would be 12 minutes LOST per DAY.
The South clock gains 15 seconds/hour; with 24 hours/day, that would be 6 minutes GAINED per DAY.

There are 60 minutes/hour, so to make these calculations a little easier to think about, I'm going to think in terms of hours instead of minutes:
After 5 days....
The North clock will have LOST (12 minutes/day)(5 days) = 60 minutes in 5 days = 1 hour LOST every 5 days
The South clock will have GAINED (6 minutes/day)(5 days) = 30 minutes in 5 days = 1/2 hour GAINED every 5 days

Thus, every multiple of 5 days will give us a relatively nice fraction (either 1 or 1/2). Looking at the answer choices, there's only one answer that's a multiple of 5....
IN 40 DAYS.....
The North clock will have LOST (1 hour/5 days)(40 days) = 8 hours LOST every 40 days
The South clock will have GAINED (1/2 hour/5 days)(40 days) = 4 hours GAINED every 40 days.
On a 12-hour clock face, 8 hours lost combined with 4 hours gained would lead to the exact SAME time, so this MUST be the answer.

Final Answer: C

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