There were 240/10 = <<240/10=24>>24 pomelos in a box.
This means that each box has 24/12 = <<24/12=2>>2 dozens of pomelos since 1 dozen is equal to 12.
The farmer shipped a total of 10 + 20 = <<10+20=30>>30 boxes.
Thus, the farmer shipped a total of 30 x 2 = <<30*2=60>>60 dozens of pomelos.
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