Firstly: 

It is not permissible for anyone who is able to fast in Ramadaan, and who has no legitimate excuse, not to fast. Not everyone who does not fast because of a concession is required to feed a poor person for every day. Rather feeding the poor is required of those who are elderly or are suffering a chronic illness for which there is no hope of recovery. 

Allaah says (interpretation of the meaning): 

“And as for those who can fast with difficulty, (e.g. an old man), they have (a choice either to fast or) to feed a Miskeen (poor person) (for every day).”

[al-Baqarah 2:184]

Ibn ‘Abbaas said: This refers to an old man or an old woman who are not able to fast, so for each day they should feed one poor person.” Narrated by al-Bukhaari, 4505. 

The person who is suffering from a chronic illness from which there is no hope of recovery comes under the same ruling as an old man. 

Ibn Qudaamah (may Allaah have mercy on him) said:  

The sick person for whom there is no hope of recovery may break the fast, and he should feed one poor person for each day, because he is like an old man. End quote. 

Al-Mughni, 4/396. 

Secondly: 

It is not essential that this poor person be an adult, rather the food may be given to a child who eats regular food, according to scholarly consensus. But the imams differed with regard to giving it to a nursing infant. The majority of scholars (including Abu Haneefah, al-Shaafa’i and Ahmad) are of the view that this is permissible, because he is a poor person who is included in the general meaning of this verse. The apparent meaning of the words of Imam Maalik is that food should not be given to a nursing infant, but he said that it is permissible to give it to a weanling. This view was favoured by al-Muwaffaq Ibn Qudaamah (may Allaah have mercy on him). 

See: al-Mughni, 13/508; al-Insaaf, 23/342; al-Mawsoo’ah al-Fiqhiyyah, 35/101-103. 

Thirdly: 

The children, wife and family of a poor person on whom he is obliged to spend may be included in this number, if they do not have enough to live on and there is no one else who can spend on them apart from this poor man. 

Hence the poor man may be given zakaah that is sufficient for him and his family. 

It says in al-Rawd al-Murbi’ (3/311): 

The two types – i.e., the poor (fuqara’) and needy (masaakeen) – may both be given what is sufficient for them and their dependents. End quote. 

Fourthly: 

As for what is to be given and how much, the poor person should be given half a saa’ (approximately one and a half kilograms) of the local staple food, whether it is rice, dates or anything else. If some condiment or meat is also given, that is better.

Al-Bukhaari narrated in a mu’allaq report from Anas (may Allaah be pleased with him) that when he grew old and was unable to fast, he did not fast and he would give bread and meat to a poor person for each day. 

It is not permissible to give the equivalent value of the food in money. 

Shaykh Saalih al-Fawzaan (may Allaah preserve him) said: 

Feeding the poor is not to be done by giving cash as you mentioned, rather it is done by giving the food that is the local staple food. So each day half a saa’ of the usual local staple food is to be given, and half a saa’ is equivalent to approximately one and half kilograms. 

So you have to give this amount of the local staple food for each day, and do not give cash, because Allaah says (interpretation of the meaning): 

“And as for those who can fast with difficulty, (e.g. an old man), they have (a choice either to fast or) to feed a Miskeen (poor person) (for every day).”

[al-Baqarah 2:184]

He specifically mentioned food. End quote. 

Al-Muntaqa min Fataawa al-Shaykh Saalih al-Fawzaan, 3/140. 

See also the answer to question no. 39234. 

And Allaah knows best.