It has been shown by \textit{Scherrer and Putter} that, when dynamics
    of dark energy is driven by a homogeneous $k-$essence scalar field $\phi$, with
    a Lagrangian of the form $L = V_0F(X)$ with a constant potential $V_0$ and $X =
    \frac{1}{2}\nabla^\mu\phi \nabla_\mu\phi = \frac{1}{2}\dot{\phi}^2$, one
    obtains a scaling relation $X(dF/dX)^2 = Ca^{-6}$ , where $C$ is a constant and
    $a$ is the FRW scale factor of the universe. The separate energy conservation
    in the dark energy sector and the constancy of $k-$essence potential are
    instrumental in obtaining such a scaling. In this paper, we have shown that
    even when considering time-dependent interactions between dark energy and dark
    matter, the constancy of $k-$essence potential may lead to a modified form of
    scaling. We have obtained such a scaling relation for a particular class of
    parametrisation of the source term occurring in the continuity equation of dark
    energy and dark matter in the interacting scenario. We used inputs from the JLA
    analysis of luminosity distance and redshift data from Supernova Ia
    observations, to obtain the modified form of the scaling.

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