The rupee today plunged to fresh low of 55.35 rupees per dollar in late afternoon trade despite RBI's measures to curb the persistent fall.The domestic unit tumbled by 32 paise to trade at fresh all-time low of 55.35 rupees .The fall was supported by the strong dollar demand from importers after the US currency strengthened in overseas markets.The rupee had resumed higher in its morning session at 54.60 rupees per dollar as against the last closing level of 55.03 rupees per dollar.The BSE benchmark Sensex index fell by 151.80 points to trade 16,031.46 points in pre-close session.