In dry, warm, closed storage, mangosteens can be held 20 to 25 days. Longer periods cause the outer skin to toughen and the rind to become rubbery; later, the rind hardens and becomes difficult to open and the flesh turns dry.
Ripe mangosteens keep well for 3 to 4 weeks in storage at 40º to 55º F (4.44º-12.78º C). Trials have shown that optimum conditions for cold storage are temperatures of 39º to 42º F (3.89º-5.56º C) and relative humidity of 85 to 90%, which maintain quality for 49 days. It is recommended that the fruits be wrapped in tissue paper and packed 25-to-the-box in light wooden crates with excelsior padding for those who wants to export it.
So this is how you do it !!