  In this work, we use a test based on the differential ages of galaxies for
distinguishing the dark energy models. As proposed by Jimenez and Loeb,
relative ages of galaxies can be used to put constraints on various
cosmological parameters. In the same vein, we reconstruct $H_0dt/dz$ and its
derivative ($H_0d^2t/dz^2$) using a model independent technique called
non-parametric smoothing. Basically, $dt/dz$ is the change in the age of the
object as a function of redshift which is directly link with the Hubble
parameter. Hence for reconstruction of this quantity, we use the most recent
$H(z)$ data. Further, we calculate $H_0dt/dz$ and its derivative for several
models like Phantom, Einstein de Sitter (EdS), $\Lambda$CDM,
Chevallier-Polarski-Linder (CPL) parametrization, Jassal-Bagla-Padmanabhan
(JBP) parametrization and Feng-Shen-Li-Li (FSLL) parametrization. We check the
consistency of these models with the results of reconstruction obtained in
model independent way from the data. It is observed that $H_0dt/dz$ as a tool
is not able to distinguish between the $\Lambda$CDM, CPL, JBP and FSLL
parametrizations but as expected EdS and Phantom models show noticeable
deviation from the reconstructed results. Further, the derivative of $H_0dt/dz$
for various dark energy models is more sensitive at low redshift. It is
observed that the FSLL model is not consistent with the reconstructed results
at redshifts less than $0.5$, however, the $\Lambda$CDM model is in concordance
with the 3$\sigma$ region of the reconstruction.
