1. Problem: $86 : 29 :: 98 : ?$. 2. Let the tens digit be $a$ and the units digit be $b$, so for $86$ we have $a=8$, $b=6$. 3. Assume a linear relation between the digits of the form $f(a,b)=p a + q b + r$. 4. For the first pair this gives the equation $8p+6q+r=29$. 5. For the second pair the value would be $9p+8q+r$. 6. Subtracting the two equations yields $(9p+8q+r)-(8p+6q+r)=p+2q$, so the second value equals $29 + p + 2q$. 7. Choose the simplest integer coefficients, take $p=1$ and $q=0$, which gives $r=29-8p-6q=29-8=21$. 8. Therefore $f(a,b)=a+21$, and for $98$ we get $f(9,8)=9+21=30$. 9. Answer: option (1) 30.