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

Can some experts show me the best solution in this problem? How will i start solving it?

OA C

Hi lheiannie07,
Let's take a look at your question.

The North clock loses 30 sec/hr and the South clock gains 15 sec/hr.
The ratio between the North clock loss and South clock gain is:
$$North\ Clock\ :\ South\ Clock$$
$$30:15$$
$$2:1$$
We can use these ratios to find when these clocks show the same time.
Since the clocks are 12 hours format, so they will show the same time when:
$$North\ clock\ loses=\frac{12}{\left(2+1\right)}\times2=\frac{24}{3}=8hours$$
$$South\ clock\ gains=\frac{12}{\left(2+1\right)}\times1=\frac{12}{3}=4hours$$

Let's find how many hours the North clock loses in a day.
North clock loses 30 seconds in one hour.
In 24 hours the North clock loses = 30 * 24 = 720 seconds = 12 minutes = 12/60 hours = 0.2 hours
The clocks will show the same time after 8/0.2=40 days

Therefore, Option C is correct.
Hope it helps.
I am available if you'd like any follow up.

lheiannie07 wrote: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