= Solution
The right panel of the figure in <past-exam-of-the-short-options-paper-of-the-physics-prelims-of-the-university-of-oxford/2019/s2/1/b/solution> has <luminosity> increasing upwards and <effective temperature> decreasing to the right. An old <globular cluster> contains a low-mass <main sequence>, a <main-sequence turnoff>, <subgiants>, a <red giant branch>, a <horizontal branch>, an <Asymptotic giant branch> and a faint hot <white dwarf> sequence. Its high-mass <main sequence> is absent because those stars have evolved.
If a fraction $f_c=0.1$ of the star participates in <hydrogen burning>, with initial <hydrogen mass fraction> $X=0.7$, the available <nuclear binding energy> is $0.007f_cXM c^2$. Assuming a roughly constant <luminosity> and coeval stars,
$$
\boxed{t\simeq\frac{0.007f_cX(0.8M_\odot)c^2}{1.6\times10^{26}\,\mathrm W}\simeq1.39\times10^{10}\,\mathrm{yr}.}
$$
Taking the quoted core fraction as hydrogen fuel itself, $f_cX=0.1$, gives $1.98\times10^{10}\,\mathrm{yr}$. Stating the fuel convention matters: burning the whole stellar mass overestimates the age by about an order of magnitude. Evolving <luminosity> and detailed <stellar structure> are needed for an accurate age.
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