Most scriptures prescribe the method where the ratio is 1:4:2.
For example Devi Bhagavatam states:
Vajrâsan (diamond seat) consists in placing the feet on the two thighs
respectively and placing the fingers below the thighs with the hands
also there, and then sitting at ease. Vîrasan consists in sitting
cross on the hams in placing the right foot under the right thigh and
the left foot under the left thigh and sitting at ease with body
straight. Taking in the breath by the Idâ (the left nostril) so long
as we count "Om" sixteen, retaining it in the Susumnâ so long as we
count "Om" sixty-four times and then exhaling it slowly by the Pingalâ
nâdi (the right nostril) as long as we count "Om" thirty-two times.
(The first process is called Pûraka, the second is called Kumbhaka,
and the third is called Rechaka). This is called one Prânâyâma by
those versed in the Yogas. Thus one should go on again and again with
his Prânâyâma. At the very beginning, try with the number twelve, i.
e., as we count "Om" twelve times and then increase the number
gradually to sixteen and so on. Prânâyâma is of two kinds :-- Sagarbha
and Vigarbha. It is called Sagarbha when Prânâyâma is performed with
repeating the Ista Mantra and Japam and meditation.
Book 7, Chapter 35
Arthur Avalon, in the introductory passages of the book "Mahanirvana Tantram", gives the same ratio:
All beings say the ajapa Gayatri, which is the expulsion of the breath
by Hangkara, and its inspiration by Sahkara, 21,600 times a day.
Ordinarily, the breath goes forth a distance of 12 fingerÕs breadth,
but in singing, eating, walking, sleeping, coition, the distances are
16, 20, 24, 30, and 36 breadths respectively. In violent exercise
these distances are exceeded, the greatest distance being 96 breadths.
Where the breathing is under the normal distance, life is prolonged.
Where it is above that, it is shortened. Puraka is inspiration, and
rechaka expira-tion. Kumbhaka is the retention of breath between these
two movements. Kumbhaka is, according to the Gheranda Sanghita of
eight kinds: sahita, suryyabheda, ujjayi, shitali, bhastrika,
bhramari, murchchha, and kevali. Pranayama similarly varies. Pranayama
is the control of the breath and other vital airs. It awakens shakti ,
frees from disease, produces detachment from the world, and bliss. It
is of varying values, being the best (uttama) where the measure is 20;
middling (madhyama) when at 16 it produces spinal tremor; and inferior
(adhama) when at 12 it induces perspiration. It is necessary that the
nadi should be cleansed, for air does not enter those which are
impure. The cleansing of the nadi (nadi-shuddhi) is either samauÇ or
nirmanu that is, with or without, the use of vija. According to the
first form, the yogi in padmasana does gurunyasa according to the
directions of the guru. Meditating on "yang," he does japa through Ida
of the vija 16 times, kumbhaka with japa of vija 64 times, and then
exhalation through the solar nadi and japa of vija 32 times. Fire is
raised from manipura and united with prithivi. Then follows inhalation
by the solar nadu with the vahni vija 16 times, kumbhaka with 64 japa
of the vija, followed by exhalation through the lunar nadi and japa of
the vija 32 times.
Lord Shiva himself gives the ratio to be 1:4:2 in the aforesaid Tantra's 3rd Chapter:
The worshipper disciple should in the like manner, with his mind well
under control, perform Anga-nyasa in accordance with the rules
thereof, commencing with the heart and ending with the hands (43).
After this, whilst reciting the Mantra Om or the Mula-mantra,
Pranayama should be performed thus: He should close the left nostril
with the middle of the fourth finger, and then inhale through the
right nostril, meanwhile making japa of the Pranava or the Mula-mantra
eight times. Then, closing the right nostril with the thumb and
shutting also the mouth, make japa of the Mantra thirty-two times.
After that gently exhale the breath through the right nostril, doing
japa of the Mantra the while sixteen times. In the same way perform
these three acts with the left nostril, and then repeat the same
process with the right nostril. O adored of the Devas! I have now told
Thee of the method of Pranayama to be observed in the use of the
Brahma-Mantra (44-48). The Sadhaka should then make meditation which
accomplishes his desire (49)
The only place where this ratio is mentioned differently (as far as my knowledge goes) is the KulArnava Tantram. Here, the whole process itself is also mentioned somewhat differently.
Here the Pranayama being done is actually part of the three purifying processes - Deha-Shoshana (drying up the body), Deha-Dahana (burning the body for purifying purpose) and Deha-PlAvana (bathing the body with the nectar flowing from Sahsrara). Here the ratio given is 3:4:3.
DvAdashAvartayan budhyA pranavntu trimAtrakam |
vAyumantah-stham rechako bhavet ||
ShanakairirayA vadhA purakam parikirtam
DvAdashAvartayan tAram vAyum madhye cha kumbhayet |
Shoshayed-vAyu-bijena deha-shoshana-miritam ||
Upon reciting Om twelve times mentally one should exhale the air
through the PingalA channel (i.e. through the right nostril). This is
known as Rechaka (exhalation). Next, Upon reciting Om mentally sixteen
times one should inhale air through the IdA channel (the left
nostril). This is known as Puraka (inhalation). Thereafter, one should
retain the inhaled air inside and chant mentally Om tewlve times.
Next, one should dry up the body by chanting VAyu Bija (or Yam). This
is known as drying up the body (Deha-Shoshana).
Chapter 15, Verses 36,37,38
Therefore, any of the above will be correct to practice, the most commonly practiced by the aspirants being the process where the ratio is 1:4:2.