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India had won the series-opener in Bengaluru by 203 runs.
Following on, South Africa were all out for 189 in their second innings in the final session of day four.
India scored a mammoth 601 for five in their first innings with skipper Virat Kohli leading the side with a majestic double hundred.
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The third and final Test will be played in Ranchi from October 19.
South Africa will return to India next year to compete in a three-match ODI series, beginning in Dharamsala on March 20.
Brief Scores:
India 1st innings: 601 for 5 declared
South Africa: 275 and 189 all out in 67.2 overs (Dean Elgar 48; Umesh Yadav 3/22, Ravindra Jadeja 3/52, Ravichandran Ashwin 2/45).