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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'sfield equations with variable gravitational and cosmological "constants" for aspatially homogeneous and anisotropic Bianchi type-I space-time. To study thetransit 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 dependentdeceleration parameter $q = - 1 + \frac{nk}{(k + t)^{2}}$, comprising a classof models that depicts a transition of the universe from the early deceleratedphase to the recent accelerating phase. We find that the time dependentdeceleration parameter is reasonable for the present day Universe and give anappropriate description of the evolution of the universe. For $n = 0.27k$, weobtain $q_{0} = -0.73$ which is similar to observed value of decelerationparameter 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 deceleratingto present accelerating phase. For $k = 0$, the universe has non-singularorigin. In these models, we arrive at the decision that, from the structure ofthe field equations, the behaviour of cosmological and gravitational constantsand are related. Taking into consideration the observational data, we concludethat the cosmological constant behaves as a positive decreasing function oftime whereas gravitational constant is increasing and tend to a constant valueat late time. $H(z)/(1+z)$ data ($32$ points) and model prediction as afunction of redshift for different $k$ and $n$ are successfully presented byusing recent data (Farooq and Ratra, Astrophys. J. 66: L7, 2013). Some physicaland geometric properties of the models are also discussed.

Bianchi type-I transit cosmological models with time dependent gravitational and cosmological constants - reexamined