The 30-scrip sensitive index (Sensex) of the Bombay Stock Exchange (BSE), which opened in the positive at 19,798.18 points, was trading at 20,140.21 points in the afternoon session, up 2.12 percent or 417.92 points from its previous day close at 19,722.29 points.
The benchmark Sensex touched a high of 20,154.84 points and low of 19,798.18 points in the intra-day.
The wider 50-scrip S&P CNX Nifty of the National Stock Exchange (NSE) was trading 2.08 percent or 124.85 points higher at 6,120.25 points.
Strong buying support in interest rate sensitive banking, realty, auto and capital goods stocks led the rally in the markets.
India's headline inflation fell to 4.89 percent in April, the lowest level since November 2009, according to official data released Tuesday.
Inflation has come within the comfort zone of the Reserve Bank of India (RBI) for the first time in almost three-and-a-half year. A sharp drop in inflation has fuelled hopes that the central bank would lower interest rates early.
The BSE realty index rallied 3.29 percent. Banking index was trading 2.89 percent higher; auto index was up 2.57 percent and capital goods index was ruling 2.52 percent higher.