A ration is a portion or an amount that is GIVEN TO a person or a group.
For example, each of the refugees could be given a ration of food, including flour, canned beans and fresh vegetables for the week.
A quota is a part or an amount that is REQUIRED FROM each person or group.
For example, each person on the sales team has a quota. They must each contact 4 new customers every morning.
Hope this helps.