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Cheteshwar Pujara and Ajinkya Rahane led an India fight-back as they helped their side build a 126-run lead against Australia in the second Test.

Australia added 39 for four wickets to their overnight total as they made 276 to the home side's first innings 189.

The hosts lost two wickets in erasing their 87-run deficit and were 120-4 before Pujara and Rahane put on an unbroken 93 on day three in Bangalore.

The duo batted the whole last session as India reached 213-4 by the close.

The partnership between Rahane and Pujara, who was was dropped on four by Steve Smith off spinner Nathan Lyon, was India's highest of the series so far, after a comprehensive defeat in the opening Test.

Opener KL Rahul also played a part in an improved batting display with 51.

"It was a little bit easier than the first innings," said Rahul. "The wicket was the best to bat on today. I wanted to cash in and get a good start for the team.

"We went in with a clear intent to use our feet and rotate the strike.

"It was a fantastic partnership between Pujara and Rahane and the team really needed it."

Australia lead the series 1-0 after winning the opening Test of the four-match series.