General approach to task 17 in EGE Mathematics

58564(q^4-1)/(q-1)=Sq^4
106964(q^2-1)/(q-1)=Sq^2, where q=1+r/100
keep in mind that (q^4-1)= (q^2-1)(q^2+1)
In second equation (q^2-1)= (q-1)(q+1)
Proceed as follows

58564(q^2-1)(q^2+1)/(q^2-1)=Sq^4/(q+1)
106964 = Sq^2/(q+1)
Finally we get
58564(q^2+1) = 106964 q^2 => general approach to tasks of such a kind

q^2=58564:(106964-58564) => q=1.1  => r = 10%