The 'Mean'est Problem ever!

$\dfrac{X}{p}= 70 \rightarrow X= 70p$ (Sum of scores of first class)

$\dfrac{Y}{n}= 92 \rightarrow Y= 92n$ (Sum of scores of second class)

$\dfrac{X+Y}{p+n}= 86 \rightarrow \dfrac{70p+92n}{p+n}= 86$

$70p+92n=86p+86n \rightarrow 6n=16p$

$\dfrac{p}{n}= \dfrac{6}{16}= \boxed{0.375}$

The $S_F$ denotes the score of $F$ th student in class

I USED THE WAY OF THE OF MY ANCIENT GREEK AND ITALIAN ANCESTORS

The mean of the first class can be given by: $\displaystyle \frac{t_p}{p} = 70$

Mean of second class: $\displaystyle \frac{t_n}{n} = 92$

$t_p + t_n = 70p+92n$

Average: $\displaystyle \frac{70p+92n}{p+n} = 86$

Simple algebraic manipulation gives $\frac{6}{16}$