Let's say the test is 100 points.
The 70% mean means that the mean for the 30 students was 70 points. That means 2100 points were scored between all 30 students. (70·30=2100)
20 boys had a mean of 62% or 62 points for our test. That means the boys earned 62·20 points, or 1240 points.
That then means the girls earned 2100 - 1240 points, or 860 points.
Since there are 10 girls, 860/10 = 86 or 86% mean on the test.
Girls rock!