Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S26 / 1 / 4 / Solution

At D, $M_V=20.3-15.09=5.21$. Ignoring differential bolometric corrections, $L/L_{\odot }\simeq 10^{-0.4(5.21-4.74)}\simeq 0.65$, and $L\propto M^4$ gives $\boxed{M_D\simeq 0.90M_{\odot }}$. If accessible fuel fraction is similar, lifetime scales as $M/L\propto M^{-3}$. Normalizing to a solar main-sequence lifetime about 10 Gyr gives an age near $\boxed{14\mathrm{Gyr}}$.

This is much older than the Sun's current approximately 4.6 Gyr and close to the cosmological age scale. The approximate estimate is not evidence for a cluster older than the Universe: bolometric corrections, abundance, accessible hydrogen fraction and the crude mass-luminosity law limit precision. The stated 26.7 MeV conversion and an assumed core fuel fraction can supply the order-of-magnitude solar lifetime; they do not by themselves specify the burned fraction or composition precisely.