Exchanging torn bank notes for half of their value
Question

                If there are torn banknotes that people will not accept to deal with, there are some banks which will exchange them for half of their value, so they will take a torn note that is worth one hundred riyals and give you fifty riyals. What is the ruling on this?.
Praise be to Allah.
      We put this question to Shaykh ‘Abd al-Rahmaan al-Barraak 
      (may Allaah preserve him), and he answered as follows: 
The basic principle 
    regarding the exchange of gold for gold and silver for silver is that equal 
    amounts must be given, like for like. It makes no difference whether 
    something is faulty or broken, etc. 

    Banknotes nowadays have taken the place of gold and silver in 
    that the value of things is measured in terms of them. 

    But we cannot apply all the rulings on gold and silver to 
    banknotes, because bank notes do not have any value in and of themselves, 
    rather their value is conferred by the state which issues them. 

    Hence I say that there is nothing wrong with exchanging torn banknotes for half of their value, because they have now lost their value (i.e., by becoming torn).