The Indian rupee continued to plunge and hit a new lifetime low closing of 74.39 against the dollar on sustained demand for the dollar.

This was against a close of 74.07 to the dollar on Monday, which was also a new record low for the rupee.

Indian equity benchmarks resumed decline, after small gains on Monday, led by massive losses in Tata Motors after the luxury carmaker said it was closing production because of weak demand in China.

The S&P BSE Sensex dropped 0.51 percent or 175 points to 34,299 and the NSE Nifty 50 Index declined 0.45 percent or 47 points to 10,301.

Today's drop came also on the back of a fall in the rupee. Analysts see the rupee continued to weaken on worries over a rising trade and current account deficit.

The RBI may intervene should the rupee fall more sharply. In the past, the country's central bank has stated that their intent would always be to reduce volatility.

Check rupee rates against other currencies here