  Time variable $\Lambda$ and $G$ are studied here under a phenomenological
model of $\Lambda$ through an ($n+2$) dimensional analysis. The relation of
Zeldovich (1968) $|\Lambda| = 8\pi G^2m_p^6/h^4$ between $\Lambda$ and $G$ is
employed here, where $m_p$ is the proton mass and $h$ is Planck's constant. In
the present investigation some key issues of modern cosmology, viz. the age
problem, the amount of variation of $G$ and the nature of expansion of the
Universe have been addressed.
