Let [tex]b_1,b_2,\ldots,b_{20}[/tex] be the 20 marks of the boys, and [tex]g_1,g_2,\ldots,g_{10}[/tex] be the 10 marks of the girls.
We know that the global mean was 70, meaning that
[tex]\dfrac{b_1+b_2+\ldots+b_{20}+g_1+g_2+\ldots+g_{10}}{30}=70[/tex]
Multiplying both sides by 30 we deduce that the sum of the scores of the whole classroom is
[tex]b_1+b_2+\ldots+b_{20}+g_1+g_2+\ldots+g_{10}=2100[/tex]
By the same logic, we work with the marks of the boys alone: we know the average:
[tex]\dfrac{b_1+b_2+\ldots+b_{20}}{20}=62[/tex]
And we deduce the sum of the marks for the boys:
[tex]b_1+b_2+\ldots+b_{20}=1240[/tex]
Which implies that the sum of the marks of the girls is [tex]2100-1240=860[/tex]
And finally, the mean for the girls alone is
[tex]\dfrac{860}{10}=86[/tex]
