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Shami returned 3 for 27 and 4 for 31 as Bangladesh were bowled out for 150 and 213, while Agarwal scored 243 - his second double-century in just 12 Test innings - when India put up 493 for 6 declared.
His seven-wicket haul meant Shami moved up eight spots in the rankings to a career-high No. 7, three positions below Jasprit Bumrah and three spots above No. 10 R Ashwin. Shami's current tally of 790 rating points is also the third best for an India quick ever, only behind Kapil Dev (877) and Bumrah (832).
Agarwal, meanwhile, finished just outside the top ten, which includes team-mates Virat Kohli at No. 2, Cheteshwar Pujara at No. 4, Ajinkya Rahane at No. 5 and Rohit Sharma at No. 10. The 28-year-old batsman has had a spectacular start to his Test career, totalling 858 runs in just eight games so far, his runs coming at an average of 71.50, with three centuries and three half-centuries.
From Bangladesh's point of view, it was a disappointing start to the World Test Championship campaign, as they lost the first of two Tests inside three days. Mushfiqur Rahim, though, did well with the bat, scoring 43 and 64, which helped him move up five spots to No. 30, while Abu Jayed, the fast bowler who picked up four wickets in the Indian innings, moved to the 62nd position, a jump of 18 spots.
Among the other Indians who did well in Indore, Ravindra Jadeja advanced to be joint-35th among batsmen (with Australia's Marnus Labuschagne) after scoring an unbeaten 60, while there were one-spot gains for Shami's fast-bowling mates Ishant Sharma and Umesh Yadav, up to No. 20 and No. 22 respectively.
The Indore win meant that India carried forward their perfect start to the World Test Championship, currently on a maximum of 300 points from six Tests, with New Zealand Sri Lanka, who have both played just two games so far, way behind on 60 points apiece. The second and final Test of the series will be played under lights in Kolkata from November 22.