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Sent into bat first, South Africa scored 105 for the loss of six wickets in the allotted 20 overs.
Then, the rain interrupted the match and the Match Referee set a target of 73 runs to win in 13 overs for Bangladesh.
Bangladesh reached the winning target making 75 for the loss of three wickets when they had five balls to spare.
Salma Khatun remained unconquered with 27. Her 14-ball innings was decorated with four fours and a six.
Shukhtara Rahman remained undefeated with 15 off 12 balls amid two fours while Farzana Haque scored 15 off 17 balls including two boundaries.
Rumana Ahmed was the other notable rum maker for Bangladesh. She knocked 14 off 21 balls.
SM Benade took one wicket for five runs.
Earlier, SM Benade also shone with the willow. She was the day's top scorer with 37. Her 30-ball knock was studded with three over boundaries and two boundaries.
Besides, M du Preez notched up 18 off 15 balls.
Salma Khatun bagged a couple of wickets instead of 21 runs while Rumana Ahmad and Khadiza Tul Kubra took one wicket each for 10 and 24 runs respectively.