Georgia's test started with 75 problems and then Georgia completed 10, 75 - 10 = <<75-10=65>>65 problems.
After 20 minutes she completes twice as many problems, 10 x 2 = <<10*2=20>>20.
With 40 minutes left she has completed 10 + 20 problems = <<10+20=30>>30 problems.
From the original 75 problems she has solved 30, 75 - 30 = <<75-30=45>>45 problems she has left.
#### 45