  In the background of a homogeneous and isotropic spacetime with zero spatial
curvature, we consider interacting scenarios between two barotropic fluids, one
is the pressureless dark matter (DM) and the other one is dark energy (DE), in
which the equation of state (EoS) in DE is either constant or time dependent.
In particular, for constant EoS in DE, we show that the evolution equations for
both fluids can be analytically solved. For all these scenarios, the model
parameters have been constrained using the current astronomical observations
from Type Ia Supernovae, Hubble parameter measurements, and baryon acoustic
oscillations distance measurements. Our analysis shows that both for constant
and variable EoS in DE, a very small but nonzero interaction in the dark sector
is favored while the EoS in DE can predict a slight phantom nature, i.e. the
EoS in DE can cross the phantom divide line `$-1$'. On the other hand, although
the models with variable EoS describe the observations better, but the Akaike
Information Criterion supports models with minimal number of parameters.
However, it is found that all the models are very close to the $\Lambda$CDM
cosmology.
