Why is Hanuman ji applied vermilion-
Some Hindu gods are pleased and like some particular thing or things. When these things are offered to them, they are pleased. For example Lord Shiva is pleased when someone offers bel leaves to him, Lord Ganesh is pleased with Durva (A kind of Grass). Lord Vishnu is pleased with Tulsi. Likewise monkey god Hanumanji is pleased with Sindur (vermilion).
The following is the story showing why Hanuman ji is applied (Smeared) Sindur -
One day Hanuman ji was hungry, so he went to Mata sita and said,"Mother, I am hungry. Kindly give me some thing to eat. Sita said affectionately, after taking my bath, I shall give you Modak (a kind of sweet) to eat." Hearing Sita's words, Hanuman began to chant 'Ram, Naam' and waited for Sita to come back after taking her bath. After taking bath Sita applied vermilion on her head. Hanuman asked her, " Mother, why are you are applying this vermilion on your head?" Sita replied," I apply sindur for the long life of my husband, Lord Ram."
Hanuman began to think over what Sita had said. Applying sindur, increases the life of my Lord. He got up all of a sudden and smeared sindur on his own body thinking that it would increase the age of Lord Ram and He (Ram) will become immortal.
Then Hnuman went to the Raj Sabha of Lord Ram. Ram saw Hanuman with vermilion on his entire body and began to laugh and asked ,"Why have you applied sindur on your body ?" Hanuman explained to him the reason." Lord Ram smiled at his innocence and said," Today is Tuesday. I shall be pleased with the person who will apply sindur and oil to my devotee Hanuman on this day. This action of theirs will fulfil their desires."
Since then people apply and offer sindur to god Hanuman.
(Source- Hanuman Ank Page 356)
"May god Hanuman bless You !"
*****
"May god Hanumanji fulfill your desires !"
******
Other Posts you will like to read -
(8) Remedial measures for different problems.(14.2.4) Hanuman Chalisa/ Importance of hanumanchalisa
(14.2.5) Hanuman Chalisa as Remedial Measure