Since the Hindu calendar is based on the lunar calendar, there is a difference of 11 days between the earth year and the lunar year.
It is a fact that the solar year is made up of 365 days and about 06 minutes and the lunar year is made up of 354 days.
To adjust this difference Adhik Maas is added regularly. This is how Makar Sankranti (kite flying festival) is always on 14th January.
First of all I am not sure what makes you think that this practice is 'added' at some point. There are references to adhika masa, also knows as Purusottama masa in parama purana as you can find here and other places on the internet.
Seems it is clear to you on why this is practiced but for the sake of completeness I am including it here from the above site:
The Lunar year consists of 12 lunar months each consisting of 30
tithis but this does not add up to 30 solar days since in the course
of a lunar month a tithi will vary from about 19 hours to 26 hours
with an average length of 23h 37m 28s. The lunar month would be
29.530589 days. Because the Lunar year is 360 tithis long, that is only 354.36 solar days long after only three years it would be about
one month out of phase with the solar year. However to keep it in
phase with the solar year, and thus with the seasons and religious
observances, a leap month (adhika-masa) is introduced. The
introduction of the adhika-masa is not artificial, but a natural
occurrence (Metonic cycle) because about every third year there will
be experienced the phenomena of two new Moons while the Sun transits
through one Rasi. And since the lunar month is defined as the length
of time between successive new Moons and that there can only be one
Lunar month corresponding to a solar month, the extra lunar month
becomes a leap month. Thus the solar and lunar years would continue to
stay in phase perpetually, their difference never being more than
about 22 days. In the first year they would be out of phase by 11
days, the second year out of phase by 22 days, the third year the leap
month brings them back in phase, the fourth year out of phase by 11
Now what happens if this practice is not followed. The site also addresses this saying:
'If the Vedic Lunar year were not linked to the solar year then within
only a few years there would be very noticeable differences in a
change of seasons in relation to the calendar. By an accumulation of
about 11 days per year it would not take long before a festival
associated with the summer such as Krishna Janmastami would be
observed in the spring when Gaura Purnima should be observed. That
would be absurd'
So from the reference to Padma Purana and the consequences of not following it, it seems that this is natural part of Vedic calculations rather a later invention. Unless you cite proper references that it is added at a later time and how the consequences discussed above were dealt prior to it's introduction, the question of when it was introduced seems out of context.
The ancient Hindu seers have had a comprehensive study of time. The minute details covered by those fantastic minds in reckoning time is bewildering. The Hindu calender is based on the age of Bramha, the Creator. The life span of Creator Lord Bramha is 100 years. His age now is 51 years. Each day of Lord Bramha is designated by a Kalpa. Each Kalpa comprise of 14 Manus and each Manu consist of 71 Mahayuga. 1000 such Mahayugs completes Lord Bramha's 1 day. At present, we are in the 28th Mahayug.
Since the calender is based on the phases of the moon, the twelve as above take 354 days, 8 hours and 34.28 seconds. This creates a difference of 10 days, 21 hours and 35.16 seconds from the actual solar year (365 days, 6 hours, 9.54 seconds)
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