The apex bank on Tuesday cut the benchmark interest rate by 25 bps to 7.25 per cent for the third time this year to steer economic growth.
Meanwhile, the benchmark BSE Sensex on Tuesday plunged by 661 points today to 27,188.38 as the RBI took a cautious stance on the economic recovery.
However, the local currency recovered smartly for a brief period to hit a high of 63.66 during the trade before sliding back to end at 63.82, showing a fall of 0.12 paise, or 0.19 per cent.
Globally, the dollar was broadly lower against basket currencies amid uncertainty over Greek debt woes.
The US dollar index was trading substantially lower by 0.69 per cent at 96.85.
Rate cut to spur housing demand: Realty firms
Rupee closes 12 paise higher against dollar on rate cut hope
RBI effect: SBI, Allahabad cut lending rates
RBI lowers growth forecast to 7.6%
Rupee closes marginally lower by 2 paise at 63.82