= Solution
For ideal transfer of the <proton> bunch's <kinetic energy> to the witness bunch,
$$
N_p(62.5\,\mathrm{GeV})=N_e(112.5\,\mathrm{GeV}).
$$
Thus
$$
\boxed{N_p/N_e=1.8.}
$$
This is a minimum driver population for unit efficiency and full depletion under the stated <energy> budget. If only a fraction $\eta$ is usefully transferred, the required ratio becomes $1.8/\eta$. The equality to the <transformer ratio> uses the same ideal matching assumption as part <S19/3/b>.
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