c
(c) For \(80\) minutes, number of half lives of sample \(A = {n_A} = \frac{{80}}{{20}} = 4\) and number of half lives of sample

\(B = {n_B} = \frac{{80}}{{40}} = 2.\)

Also by using \(N = {N_0}{\left( {\frac{1}{2}} \right)^n}\)

==> \(N \propto \frac{1}{{{2^n}}}\)

==> \(\frac{{{N_A}}}{{{N_B}}} = \frac{{{2^{{n_B}}}}}{{{2^{{n_A}}}}} = \frac{{{2^2}}}{{{2^4}}} = \frac{1}{4}\)