  The present study reexamines the recent work of Pradhan et al. (Indian J.
Phys. 88: 757, 2014) and obtained general exact solutions of the Einstein's
field equations with variable gravitational and cosmological "constants" for a
spatially homogeneous and anisotropic Bianchi type-I space-time. To study the
transit behaviour of Universe, we consider a law of variation of scale factor
$a(t) = \left(t^{k} e^{t}\right)^{\frac{1}{n}}$ which yields a time dependent
deceleration parameter $q = - 1 + \frac{nk}{(k + t)^{2}}$, comprising a class
of models that depicts a transition of the universe from the early decelerated
phase to the recent accelerating phase. We find that the time dependent
deceleration parameter is reasonable for the present day Universe and give an
appropriate description of the evolution of the universe. For $n = 0.27k$, we
obtain $q_{0} = -0.73$ which is similar to observed value of deceleration
parameter at present epoch. It is also observed that for $n \geq 2$ and $k =
1$, we obtain a class of transit models of the universe from early decelerating
to present accelerating phase. For $k = 0$, the universe has non-singular
origin. In these models, we arrive at the decision that, from the structure of
the field equations, the behaviour of cosmological and gravitational constants
and are related. Taking into consideration the observational data, we conclude
that the cosmological constant behaves as a positive decreasing function of
time whereas gravitational constant is increasing and tend to a constant value
at late time. $H(z)/(1+z)$ data ($32$ points) and model prediction as a
function of redshift for different $k$ and $n$ are successfully presented by
using recent data (Farooq and Ratra, Astrophys. J. 66: L7, 2013). Some physical
and geometric properties of the models are also discussed.
