A possible resolution of tension between {\it Planck} and Type Ia
  supernova observations
  There is an apparent tension between cosmological parameters obtained from
{\it Planck} cosmic microwave background radiation observations and that
derived from the observed magnitude-redshift relation for the type Ia supernova
(SNe Ia). Here, we show that the tension can be alleviated, if we first
calibrate, with the help of the distance-duality relation, the light-curve
fitting parameters in the distance estimation in SNe Ia observations with the
angular diameter distance data of the galaxy clusters and then re-estimate the
distances for the SNe Ia with the corrected fitting parameters. This was used
to explore their cosmological implications in the context of the spatially flat
cosmology. We find a higher value for the matter density parameter, $\Omega_m$,
as compared to that from the original SNLS3, which is in agreement with {\it
Planck} observations at $68.3\%$ confidence. Therefore, the tension between
{\it Planck} measurements and SNe Ia observations regarding $\Omega_m$ can be
effectively alleviated without invoking new physics or resorting to extensions
for the standard concordance model. Moreover, with the absolute magnitude of a
fiducial SNe Ia, $M$, determined first, we obtained a constraint on the Hubble
constant with SNLS3 alone, which is also consistent with {\it Planck}.
