There is a reference in Mudgala Purana regarding the origin of Chathurthi Thithi. Once Brahma, the Creator of the universe meditated upon Lord Ganesa after he had created the Universe, in order to attain success in his work. At that very moment the ultimate Prakrti, Mahamaya, the Goddess appeared from his mouth. The Goddess had four legs, four arms and four lovely faces. The creator was very happy to see her. That Goddess prostrated herself at the feet of the creator, eulogized Him with various hymns and stated –“O Lord of the Universe, I am born from your mouth; hence you are my father. Please instruct me on what I should do. O Lord, my salutations to your lotus- like – feet. Please allot some place for my residence and provide me with things for my enjoyment “The creator initiated her into the six lettered Mantra (Vakratundaya Hum).
The Goddess followed his instructions and started her Japa while meditating upon Lord Ganesa with full concentration. She practised severe penance for a long period of one thousand celestial years. Lord Ganesa was pleased and appeared before her and said – “O great lady, I am extremely pleased with your devotion. Ask for any boon.”..The goddess prostrated Ganesa and said – “If You are really pleased. O compassionate Lord, grant me Your complete devotion towards me. Kindly make me competent to create the universe as instructed by Brahma. Your Grace may always be upon me and eternally I may not be separated from You.”
Lord Ganesa said – “Be it so. You will be capable of bestowing all the four ultimate objects of life upon my devotees. You will always be dear to me. You will be the mother of all the lunar dates and known by the name Chathurthi. Your left portion will be black and right portion white. I will specially protect those who will perform vow on Chathurthi and there will not be any other vow as great as that of yours.”Saying so Lord Ganapati disappeared. Chathurthi, the mother of all Tithis, started her work of creation while meditating on Ganapati.
All of a sudden her body appeared in two colours – the left portion black and right portion white. She was amazed. She again remembered Ganesa and was just about to start creation work that the Tithi Pratipada came out from her mouth. Similarly Dvitiya the second date, came from her nostrils, Tritiya from her breasts, Panchami from her fingers, Shashti from her heart, Saptami from her eyes, Ashtami from her arms, Navami from her stomach, Dasami from her ears, Ekadashi from her throat, Dwadashi from her legs, Trayodashi from her udders, Chathurdashi from her ego, Full moon day(Pournami) from her mind and Amavasya, the New Moon day from her tongue.
Both the Chathurtis accompanied, by all other Tithis started their penance muttering the name of Ganesa. They continued this way for one year. Lord Ganesa felt propitiated and appeared. During midday time, he approached bright Caturthi and spoke – “Ask for boon.” The bright Chathurthi said – “O Lord Ganesa, You always make Your residence in my heart and give me Your eternal devotion.” The compassionate Ganesa granted this boon to her saying – “You happened to have My vision during midday time, so the gods like Siva, etc., will remember Me and meditate upon Me at the time of noon.
On bright Chathurthi, My devotees will perform your vow. Whosoever will observe fast and worship you on this day, his accumulated actions and fruits thereof, will be wiped out and I will grant them everything. You would be named Varada (the giver of boons). Saying so the Lord Ganesa disappeared and bright Chathurthi the goddess was known since then as Varada. She became a darling of Lord Ganesa.
He who does worship on that day with prescribed rules and materials and breaks his/her fast on Pancami, is sure to get Dharma, Artha, Kama and Moksha. He/She gets his/her desire fulfilled and in the end attains the abode of Lord Ganesa.
Then Lord Ganesa went to the dark Chathurthi at the time of arising of moon when a quarter of the night was passed and said- “ O fortunate lady, ask for a boon. I will fulfill every desire of yours.” Having the vision of Lord Ganesa and feeling gratified with His words, the dark Chathurthi fell at His feet, worshipped Him as prescribed in the scriptures. She eulogized Him and submitted – “O auspicious Lord, if You are pleased with me, kindly grant me Your staunch devotion. I always may be dear to You and should never be separated from You.”
The Lord was quite pleased with her and granting her desired boon, said – “ You will always be dear to Me and never get separated from Me. You have acquired My grace after moon- rise during night. Therefore whenever there will be Chathurti at the time of moon-rise, the time will be most auspicious and you will be dear to me. By my grace you will be quite capable of removing all the obstacles and miseries of the devotees who will perform the vow without taking food or even water. You will be competent to grant them all the four objects of life. You will destroy all their actions along with their past karma. They will enjoy in this world every comfort and free from the shackles of birth and death, will attain to My abode which is very difficult for even the Yogis. O goddess, the remover of calamities, undoubtedly by My grace you will be distributing bliss and pleasure among My devotees.
It is important to note that Sankatahara Chathurthi Vrta is observed on the fourth lunar day in the Waning phase of Moon while Ganesh Chathurthi which is celebrated annually occurs during the waxing phase of the Moon.As the above story indicates both the Lunar days which occur on the fourth day from either the New Moon or Full Moon are auspicious to Lord Ganesa and any prayer or ritual addressed to Ganesa on that day has the potential to confer immense benefits on devotees.