By reading this Hadees Mubarikah, I came to know that, Fasting on Day of Ashura is not mandatory. Its option to Fast on that day, if any one don’t Fast, there is no penlty for that.
This Hadees is taken from
Book 31: Fasting Hadith 117 (Volume 3)
It is Narrated to ‘Aisha:
(The tribe of) Quraish used to fast on the day of Ashura’ in the Pre-lslamic period, and then Allah’s Apostle ordered (Muslims) to fast on it till the fasting in the month of Ramadan was prescribed; whereupon the Prophet said, “He who wants to fast (on ‘Ashura’) may fast, and he who does not want to fast may not fast.”