  We present a new FPTAS for the Subset Sum Ratio problem, which, given a set
of integers, asks for two disjoint subsets such that the ratio of their sums is
as close to $1$ as possible. Our scheme makes use of exact and approximate
algorithms for the closely related Partition problem, hence any progress over
those -- such as the recent improvement due to Bringmann and Nakos [SODA 2021]
-- carries over to our FPTAS. Depending on the relationship between the size of
the input set $n$ and the error margin $\varepsilon$, we improve upon the best
currently known algorithm of Melissinos and Pagourtzis [COCOON 2018] of
complexity $O(n^4 / \varepsilon)$. In particular, the exponent of $n$ in our
proposed scheme may decrease down to $2$, depending on the Partition algorithm
used. Furthermore, while the aforementioned state of the art complexity,
expressed in the form $O((n + 1 / \varepsilon)^c)$, has constant $c = 5$, our
results establish that $c < 5$.
