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 is the KulArnava Tantram. Here, the process itself is also somewhat different. It is actually part of three 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 |
Munchet pingalayA vAyumantah-stham rechako bhavet ||
ShodashAvartayan tAram purayedvAhyamArutam |
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.