What is the neutron: proton ratio for the nucleus ${}_{82}{}^{206}\mathrm{Pb}$?

The 206 at the top left of the symbol is the mass number of the isotope, which indicates the total number of neutrons (total of neutrons and protons) in the nucleus. 

The number in the lower left is the atomic number, which shows only the number of protons. Therefore, a simple subtraction of 206-82 shows that the 124 particles in the nucleus must be neutrons.

Therefore the neutron : proton ratio in ${ }_{82}^{206}\mathrm{Pb}$ is 124 : 82 = 62 : 41.

Hence, option A is correct.