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Goals from Kwame Boahene, Nii Adjei and Ismail Abdul Ganiyu saw Kotoko hammer RTU 3-1.
Boahene's goal was cancelled out by Abdulai Mohammed Hardi in the 21st minute before Nii Adjei restored Kotoko’s lead.
READ MORE: Watch how Kotoko defeated Asec to win Otumfuo Cup
And Ganiyu put the game beyond the reach of the RTU with the third in the 79th minute from the spot kick, after Emmanuel Gyamfi had been fouled.
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Meanwhile, AshGold defeated second-tier outfit Young Apostles by a goal to nil.
Mark Agyekum tapped in from close range by connecting to a pass from Stephen Owusu Banahene four minutes into the second half to send the Miners to the next stage.
Some lower division clubs sent three Premier League sides packing namely Aduana Stars, Karela United and Elmina Sharks.
Below are results of round 32 matches played on Wednesday.
Medeama 2-1 Bibiani Gold stars
Asante Kotoko 3-1 RTU
Aduana 2-2 Berekum Arsenal**
BA United 2-1 Kintampo
Elmina Sharks 0-1 Heart of Lions
Mighty Jets 1-3 Proud United
Karela United 1-1 Nzema Kotoko **