Cosmic age test in inhomogeneous cosmological models mimicking $\Lambda$CDM on the light cone

The possibility of reconstructing a spherically symmetric inhomogeneous Lemaitre-Tolman-Bondi (LTB) model with $\Lambda$CDM observations has drawn a lot of attention. Recently, a LTB model having the same luminosity-distance and light-cone mass density as the $\Lambda$CDM model was reconstructed. We calculate the cosmic age at our position in this model, and get the age $t_{LTB}<11.7$Gyr in 2$\sigma$ confidence level from the Seven-Year WMAP observations. This result is inconsistent with some Milky Way observations.