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Despite Tilak Varma's 32 off 17 balls, KKR scored a comfortable victory in the end. Russel, Varun Chakravarthy and Harshit Rana claimed two apiece for the winners.
With Chakravarthy taking 2/17 and Russell picking 2/34, KKR sent half the Mumbai side packing inside 13 overs, before restricting them to 139/8 in the stipulated 16 overs.
KKR jumped to second spot in the standings with 10 points from seven games, while RCB remain at the bottom with just two points from eight outings.
Chasing a target of 162, Salt added 120 with captain Shreyas Iyer for the unbroken thrid wicket as KKR romped home in 15.4 overs.
The South African players came out of the semifinal defeat with their heads held high.
Left-arm spinner Ravindra Jadeja picked up 5/33 as the Proteas were bowled out for 83 in 27.1 overs.
The Dutch seamers varied their pace and extracted bounce from a slow wicket at Kolkata's Eden Gardens to turn up the heat on Bangladesh.
Gujarat Titans and Chennai Super Kings will meet in the first Qualifier while LSG will play the Eliminator against the fourth-placed side.
Chasing a stiff target of 236, KKR could manage only 186/8. Ajinkya Rahane took Eden Gardens by storm with a sensational 29-ball unbeaten 71 while Shivam Dube muscled his way to another scintillating half-century in CSK's ' imposing 235/4.
KKR coach Chandrakant Pandit said it was very difficult for the rival batters to pick the 19-year-old leggie.
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