Hanuman is the truest devotee of Rama. His devotion is to Rama is what mankind has never seen again.
Once, Sita was applying Sindoor in her hair looking at her, curious and innocent Hanuman asked her the reason for doing it.
Sita laughed at his innocence and replied that it was customary for long life and well being of her husband, Lord Rama. Hanuman, an ardent devotee of Rama thought if a pinch of sindoor in the hair can increase the Lord’s life then why not apply it on the entire body.
With the thought of Rama’s well being Hanuman then applied sindoor all over his body.
Seeing this innocence and unmatched devotion of Hanuman, Lord Rama was overwhelmed and gave him a vardan (blessings) that whenever devotion will be considered, Hanuman’s name will be taken first. Also, whoever will pay respect to Hanuman on Tuesday, not only will his/her wishes come true but will also be dear to Lord Rama himself.
Hence, it is a custom to shower the Bajrang Bali with Sindoor and he who does so will be blessed by Lord Rama himself.