In this scenario, which coin is more valuable? There are two coins, Coin A and Coin B. You can transfer Coin A for Coin B or Coin B for Coin A only in the two following ways:

Give 100 Coin A for 10 Coin B

Or

Give 10 Coin B for 50 Coin A

In this situation, which of the coins is worth a higher value? A friend of mine presented this problem and we were unable to find a solution. Any thought?
The word 'valuable' is not well defined in this question.

If I am willing to buy an apple from you for \$1 and but I am only willing to sell an apple to you for \$4 which is more valuable: An apple or \$2? You cannot tell because neither option is sufficient to get the other option by trade.

You are faced with the same dilemma in your problem. There are different prices at which to sell and buy so neither one of the options is clearly more valuable.

EDIT: 
As @Adam Bailey points out in his excellent answer in this situation even though the exact value ratio is ill defined, it is clear that coin B is more valuable than coin A, because you can exchange one coin B for five coin A, thus you can get more by chosing coin B.