  We show that the inferred merger rate and chirp masses of binary black holes
(BBHs) detected by advanced LIGO (aLIGO) can be used to constrain the rate of
double neutron star (DNS) and neutron star - black hole (NSBH) mergers in the
universe. We explicitly demonstrate this by considering a set of publicly
available population synthesis models of \citet{Dominik:2012kk} and show that
if all the BBH mergers, GW150914, LVT151012, GW151226, and GW170104, observed
by aLIGO arise from isolated binary evolution, the predicted DNS merger rate
may be constrained to be $2.3-471.0$~\rate~ and that of NSBH mergers will be
constrained to $0.2-48.5$~\rate. The DNS merger rates are not constrained much
but the NSBH rates are tightened by a factor of $\sim 4$ as compared to their
previous rates. Note that these constrained DNS and NSBH rates are extremely
model dependent and are compared to the unconstrained values $2.3-472.5$ \rate~
and $0.2-218$ \rate, respectively, using the same models of
\citet{Dominik:2012kk}. These rate estimates may have implications for short
Gamma Ray Burst progenitor models assuming they are powered (solely) by DNS or
NSBH mergers. While these results are based on a set of open access population
synthesis models which may not necessarily be the representative ones, the
proposed method is very general and can be applied to any number of models
thereby yielding more realistic constraints on the DNS and NSBH merger rates
from the inferred BBH merger rate and chirp mass.
