Mumbai, May 17: The Rupee on Tuesday tumbled down 32 paise at 77.76 in opening session. Against the US Dollar on brisk demand for US Dollar. By bankers and importers, dealers at the Foreign Exchange said. The Rupee slipped on firm Dollar against other world currencies amid strong opening in equity market, dealer informed. The Rupee unit registered days high and low at 77.71 and 77.85 respectively against the US Dollar, dealer added.