Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S26 / 2 / 5 / Solution

The trigonometric parallax gives $d=1/0.02=50\mathrm{pc}$. Neglecting extinction, the distance modulus and given bolometric correction giveUsing the specified solar bolometric magnitude,The mass estimate uses the cubic scaling normalized to solar values. A lifetime estimate additionally needs the fraction of fuel accessible to core burning. Take a core-accessible fraction $f_c=0.1$ and initial hydrogen mass fraction $X=0.7$. The supplied fusion energy givesThe alternative common solar-lifetime normalization $t\simeq 10^{10}(M/M_{\odot })/(L/L_{\odot })$ years gives $1.69\times 10^9$ years. Thus this simplified turnoff argument gives an age of order $10^9$ years, with its fuel fraction and mass-luminosity assumptions explicitly stated. It does not use a modern fitted Hyades age or a full stellar isochrone. Unresolved binaries, extinction and deviations from the homology law affect the estimate.