Note: This answer does not deal with any exchange commissions or fees, which is what the OP assumed. In the presence of exchange commissions or fees, the answer will be different.
This answer will start with the Maths, and point out some potential pitfalls that your question might have implied.
An easy way to see which exchange option is better is to ask, "how much in JPY I can get with a fixed amount of MUR?". In this case, 100 MUR sounds a good unit to use.
In option 1, assuming 34.28 MUR will get you 1 USD (see below for a caveat), and 1 USD will get you 106 JPY. This means 34.28 MUR will get you 106 JPY, and hence 100 MUR will get you (100 / 34.28) * 106 = 309.22 JPY.
In option 2, assuming 31.2 MUR will get you 100 JPY, this means 100 MUR will get you (100 / 31.2) * 100 = 320.51 JPY.
Thus, option 2 is around 3.65% better. That is, you get 3.65 JPY more for every 100 JPY you exchange.
Lookout for the rate quoted for buying/selling currency
You have put the USD-MUR exchange rate as follow:
1 USD -> MUR 34.28
Which raised an eyebrow of mine. Do you mean you get 34.28 MUR for every USD you sell to the exchange, or you have to pay 34.28 MUR for every USD you buy?
If it is the former case you have to be careful, as you are likely to pay more MUR than the quoted number to buy a currency (as exchanges need to make money for a living as well!). While in this case it doesn't change the outcome (option 2 will still be better), for the method to be generally applicable in the future you have to take that into account.