Chasing an imposing target of 283, Ramdin smashed a run-a-ball century to rescue his side from a precarious 65 for 4, but the visitors could only manag 266 for nine in their stipulated 50 overs.
The wicket-keeper batsman's 102 helped his side inch closer to the target during which he struck 10 fours and three sixes.
Asked to bat second, the Caribbean side's batting woes continued as they lost both the openers Jermaine Blackwood and Leon Johnson inside the first eight overs. The two got out on identical score of seven off 12 balls.
Skipper Kieron Pollard scored just nine off 17 balls. He struck Sharma for a mammoth six but was back in the hut, when the leg-spinner shattered his stumps two balls later, leaving his side reeling at 65 for four after 16 overs.
It was then upto Ramdin and Darren Sammy to do the repair job, who both notched up a century and half-century each.
Sammy's 67-ball 50-run knock comprised six fours and a six.
The 29-year old Ramdin, however, did not give up and continued the onslaught. He forged a 62-run stand with Jason Holder for the sixth wicket.
But it was not enough to guide the team till the end as he was back in the hut in the 45th over while going for a big shot. Ramdin was caught at deep square leg by Jasprit Bumrah off Karun Nair.
Dhawal Kulkarni was the pick of the bowlers for India A with figures of three for 39, while Jasprit Bumrah and Karn Sharma bagged two wickets each.
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