Fasting during the month of Ramadan is one of the five pillars of Islam that are of paramount significance. The Prophet (peace and blessings be upon him) said, “Islam is built upon five pillars: testifying that there is no god except Allah and that Muhammad is the Messenger of Allah, performing Prayer, paying the zakah, making the pilgrimage to the Sacred House (Hajj), and fasting the month of Ramadan” (Al-Bukhari and Muslim).
A person who is terminally ill is exempted from fasting, but he or she must offer fidyah (compensation) for that. Compensation for skipping a fast is feeding one poor person. Allah says: [For those who can do it (With extreme hardship), is a ransom, the feeding of one that is indigent] (Al-Baqarah 2:184). If he or she cannot pay fidyah, it is acceptable for a son or a daughter to pay it on her behalf.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto,Ontario, Canada, states the following: It is absolutely fine and acceptable for a child to pay the fidyah (compensation in lieu of fasting) that is due upon his/her mother. The Prophet (peace and blessings be upon him) said, “Children are the fruits of their parents’ work” and therefore parents can benefit freely from their children’s work. Furthermore, we have been ordered in the Qur’an to excel in our kind treatment towards our parents. Therefore, a child’s willingness to pay this fidyah on behalf of his/her mother, who is not financially able, is indeed an expression of such excellence. You can rest assured just as your mother will be absolved by your generosity, you will also be blessed by it tremendously. So never feel any hesitation in your action.
Now coming to the exact amount of fidyah, it all depends on where one lives. The amount payable is the cost of a proper meal. Since the standard of living varies from country to country, the amount also may vary accordingly. In Canada it has been estimated to be a minimum of seven dollars per day of fast. But if you are in the States or anywhere in Europe you should go by the standard as determined by the Muslim scholars there. So, one should act appropriately.