# A Time Calculation Problem: 3yrs or 3yrs and 1 day?

Suppose, a person A has his birthday on 30 Sept 1994 and another person B has his birthday on 30 Sept 1997, then which of the following statement would be correct and why?

The difference between the ages of the two persons is

1. Three years correct to the number of Days

2. Three years and 1 day correct to the number of Days (because of 29th Feb 1996 that comes in between)?

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Why is this tagged under logic? –  Asaf Karagila Aug 3 '12 at 9:08
@AsafKaragila I was not able to think of any tags, also it's not a Homework Question nor do I think that it has to do anything recreational mathematics –  user221287 Aug 3 '12 at 9:13

You need to be precise about what you mean by a year, but in practise all alternatives will give you 1 as the correct answer.

Either you define a year so that it has constant length, for example 365.24 days, and then you observe that the difference between the two dates differs from 3 years with less than a day. This is the approach astronomers would take in their work.

Or you define a year so that it always has a whole number of days, like in the Julian or the Gregorian calendar. Then a year will not have constant length, which is messy when you work with astronomy, but is OK for most everyday purposes. Also in that case you get the same answer of 3 years, or Alternative 1.

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It rather depends what you mean by a year, which is approximately 365.25 days. This article gives a huge range of options with more precision and specificity.

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I vote the first option. The rationale is as follows. In the case You presented, the intuition is not clear. However, assume that person A has a birthay on 30 Sept 1994, and person B on 30 Sept 3594. So the difference in years would be 1600. And in my opinion it is intuitive then to say, that the person B will be born 1600 years after person A was. If You would like to take the approach 2, then we should say that the person B will be born 1601 years plus some days after person A, as there will be approximately 400 leap days between 1994 and 3594. And this gets more complicated, as not every $4 \cdot n$ year has 29th February. Then for the sake of simplicity, I think the first option should be taken.