X(t) = 2 cos (180 πt) cos (60πt)

=cos (240 πt) + cos (120 πt)

So, spectrum of x(t) contains impulses at following frequencies: -120, 120, -60, 60

Due to sampling spectrum shifts by nfs

fs = sampling frequency = 200 Hz

n = 0 components: - 60, -120, 80, 120

n = 1 components: 140, 80, 260, 320

n = 2 components: 340, 280, 460, 520

∴ the sampled signal is passed through a LPF with cut off frequency = 100 Hz highest frequency passing through filters = 80 Hz