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Kohli (928 rating points), who hit 136 against Bangladesh in the second Test in Kolkata, reduced the gap from 25 to three points with Australian Smith (931) to retain the second spot.
Agarwal, who struck a double century in the first Test against Bangladesh in Indore, jumped one place to 10th with 700 points. He is the fourth Indian batsmen in the top 10 list. Cheteshwar Pujara (791) and Ajinkya Rahane (759) remained at fourth and fifth positions respectively.
England all-rounder Ben Stokes also reached the top 10 for the first time by jumping three places after scores of 91 and 28 against New Zealand.
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India fast bowlers Ishant Sharma and Umesh Yadav achieved career-high points after victories over Bangladesh. Ishant has 716 points but is in the 17th place, way behind his career-best seventh place achieved in July 2011. Umesh has 672 points and has jumped one place to 21st.
Senior India spinner Ravichandran Ashwin moved one place up to ninth with 772 points, while injury-sidelined Jasprit Bumrah lost one spot to be at fifth with 794 rating points.
Ravindra Jadeja, who jumped one spot to 15th among bowlers with 725 points, retained his second spot, behind West Indian Jason Holder, in the all-rounders’ rankings.
Ashwin, meanwhile, has moved down one place to fifth among the all-rounders.