35 in late trading after the central bank broke a US dollar peg kept at 108 local units.
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A state bank that usually represents the central bank was selling dollars to the market at 110.00 rupees when trading resumed.
The central bank said early morning that it was allowing limited depreciation of the rupee breaking a peg it had spent 800 million dollars to defend over the last two months.
The rupee is expected to become more market determined over the next few days and weeks.
Analysts say reducing the volume of central bank interventions is key breaking a sterilized intervention cycle that had developed over the past two months.
Updated
The rupee was at 110.75 to the US dollar in late afternoon trading with no intervention, dealer said.
Late trading saw the rupee trading at 111.35 rupees, dealers said.