The Rupee today tumbled to an all-time low of 54.99 a dollar, just one paise short of the psychological 55 level in pre-close trade due to increased demand for the American currency from banks and importers.The local unit resumed lower at 54.70 a dollar at the Interbank Foreign Exchange (Forex) Market and plunged to a new all-time low of 54.99 against the US dollar in the evening trade.Forex dealers said fresh dollar demand from banks and particularly, month-end demand from oil importers despite weakness of the dollar in the overseas market pulled down the Rupee.