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Both of the guys are born on the same day, month, and year but they have different ages. One of them is 5 months, 12 days, and 11 years old and the other is 2 months, 17 days, and 11 years old.

Why are there two different ages then?

They were born at the same time.

There is no third child.

They were born on the same time and place.

HINT 1:

They might not be on the same page here...

HINT 2:

Now that people have guessed the idea of the answer, it is one of the most popular calendars in the world. (See comments for info)

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The two boys were born on the same day.

However, their ages are:

Represented in different calendars.

- One boy's age (the one who is 2 months old) has his age calculated using the Gregorian calendar - i.e. the one we're familiar with
- The second boy's age (the one with 5 months) has his age calculated using a Lunar calendar such as the Islamic calendar.

The Gregorian calendar is a solar calendar, with each year having 365 days spread across 12 months, whereas the Islamic calendar being a lunar calendar has only 354 or 355 days spread across 12 months.

The result of this is that there will be a gradual drift in the number of months counted by both calendars over time, with an entire year being lost across a 33 year lunar cycle.

For someone who is 11 years old, this results in a difference of about 3 months, as indicated in the question.

Note that an earlier version of this answer was on similar lines, but assumed a

Lunisolar calendar

and the answer was revised based on comments from the OP.

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  • $\begingroup$ Half wrong, but it is close $\endgroup$ – maounkhan Mar 24 '18 at 17:39
  • $\begingroup$ Is it the wrong calendar, or something else that is wrong? $\endgroup$ – Phylyp Mar 24 '18 at 17:42
  • $\begingroup$ Wrong calender. $\endgroup$ – maounkhan Mar 24 '18 at 17:43
  • $\begingroup$ OK... I've updated it to be a little more generic - since there is an entire class of calendars that exhibits this property. $\endgroup$ – Phylyp Mar 24 '18 at 17:56
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    $\begingroup$ Making it easier for you, I will say that it is the 2nd or 3rd most used calendar in the world. $\endgroup$ – maounkhan Mar 25 '18 at 22:59
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A rather tongue-in-cheek answer:

Mere seconds after their birth, one of these poor guys was whisked away in a spaceship travelling at a brisk 15% of the speed of light towards Alpha Centauri. Due to time dilation, over the 11 years, 5 months, and 12 days experienced by the earth-bound guy, the rocket guy has only experienced approximately 11 years, 2 months, and 17 days.

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  • $\begingroup$ +1 for sheer cheekiness, however, time dilation at 15% c over 11 years, 5 months, and 12 days gave me 11 years, 3 months and 17 days. Where did I (or you) go wrong? emc2-explained.info/Dilation-Calc/#.Wrh1Y9NuaCQ $\endgroup$ – Jesse Mar 26 '18 at 4:33
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    $\begingroup$ @JesseBarnett it's probably rounding errors and the fact that I assumed the months were 29.5 days each. Props for going through the calculation! $\endgroup$ – Austin Weaver Mar 26 '18 at 4:37
  • $\begingroup$ An average month is 30.42 days! yes that would be it $\endgroup$ – Jesse Mar 26 '18 at 4:38
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    $\begingroup$ @JesseBarnett I used 29.5 days, because I'm lazy and google said so :) $\endgroup$ – Austin Weaver Mar 26 '18 at 4:39
  • $\begingroup$ Having the other guy several light years away introduces another problem though: who observes their ages? The crux of the problem is that there is no sensible way to define a common ”now” that would apply to two observers at astronomical distances, so whoever is checking the ages would observe a different age difference depending on his own location. That effect can be as big as $\pm 4.3 $ years, since that’s about how long it takes for information to travel from here to Alpha Centauri, or vice versa. $\endgroup$ – Bass Mar 26 '18 at 6:03
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The difference in their ages is because the older age is being calculated in the traditional Chinese calendar.

The Chinese calendar year is about 11 days shorter than the Gregorian year, so there is a leap month every 3 years to make up for that.

There are 3 such leap years before the age of 12, so that could explain the apparent 3 month difference. Assuming they are born right after a leap month: | 3 | 3 | 3 | 2.5

With East Asian age reckoning, such differences could be even larger, because age at birth is not considered to be zero. People are born at the age of one, and age is incremented on New Year's Day, not on birthdays. A baby born on Dec 31st will be 2 years old the next day.

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This the Hijri or Islamic calendar (not to be confused with Solar Hijri calendar). It is a lunar calendar that each month has 29 or 30 days depending on when the moon is found. It is cannot be lunisolar as it does not depend on the sun for anything. It contains 354 or 355 days (differs on when the moon is sighted at the end of the month). It doesn’t do all the strategies of the lunisolar calendars. In fact, it is interesting as the conversion from this calendar to the Gregorian one are through the Jewish or Hebrew calendar most of the time. You can learn more about the system here. I could not accept the answers above because they focused on a slightly different approach and wouldn’t reach the exact age used on the second boy (one with 5 months) compared to the first boy. Thank you.

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