= Solution
Set $h=k/100$ and $j=m/100$. The exact ratio is $(1+h)^p(1+j)^q$. Multiplying the two <binomial series> and retaining total degree at most two gives the <second-order relative change of a monomial>:
$$
\frac{\Delta f}{f}=ph+qj+\frac{p(p-1)}2h^2+pqhj+\frac{q(q-1)}2j^2+O((|h|+|j|)^3).
$$
Multiply by one hundred to express the change as a percentage:
$$
\boxed{pk+qm+\frac{p(p-1)k^2+2pqkm+q(q-1)m^2}{200}.}
$$
The cross term accounts for the simultaneous changes in both inputs and cannot be recovered by simply adding their separate second-order percentage changes.
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