Prem scored 80 off 127 deliveries with the help of eight fours and a six to help Kerala end their first innings at 297 all out in reply to Tripura's paltry 140.
Apart from Prem, VA Jagadeesh (43) and Sanju Samson (42) made notable contributions with the bat for Kerala.
Kerala now lead Tripura by 157 runs with two full days play still remaining in the match.
For Tripura, right-arm pacer Rana Dutta picked up four wickets for 38 while Abhijit Dey scalped three for 91.
Brief Scores:
Tripura 1st innings: 140 all out in 67 overs
Kerala 1st innings: 297 all out in 91.1 overs (Rohan Prem 80; Rana Dutta 4/38).
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