Responding to India A's 135 in the first innings, Australia A rode on Bancroft's fourth first-class century to manage 329 for nine at stumps as the hosts gained a healthy 194-run lead.
Sharing a 111-run opening partnership with skipper Usman Khawaja (33), Bancroft gave the visitors a solid start as he stitched another crucial 107-run fourth wicket stand with Callum Ferguson (54).
Left-arm spinner Pragyan Ojha (3-99) and off-spinner Aparajith (5-74) shared eight wickets apiece to give the hosts some hope at the end of the day.
The Indian fielding though was way below par as Aparajith and India Test captain Virat Kohli floored two chances to give Feguson a longer stay at the crease. Ferguson, who was on 14 and 25 went on to register a crucial half-century. On both the occasions, Shreyas Gopal (1-69) was the bowler to suffer.
At close Stephen O'Keefe (6) and Andrewe Fekete (0) were at the crease.
The manner in which Bancroft paced up his innings spoke about his patience while six wickets fell at the other end.
When the Australians resumed their innings this morning overnight batsmen Bancroft and Khawaja were holding fort.
Ojha's hard work paid off after he trapped Khawaja LBW, and then claimed two more scalps in his very next over.
Later Aparajith brokethrough as he dismissed Marcus Stoinis (10) and then tricked Bancroft, who went on sweep and landed an easy catch to Kohli at leg slip.
Egged on by the sparse local crowd, Aparajith kept up the momentum and dismissed three more Australians --- Matthew Wade (11), Gurinder Sandhu (36) and Ashton Agar (6).
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