$($b$)$ A continuous$-$time sinusoid signal $\backslash ($ x$($t$)\backslash )$ of unknown frequency is sampled by an impulse train of period $10$ ms $.$ Then, the resulting sampled signal is applied to an ideal lowpass filter with a cutoff at $50$ Hz $.$ The output of the filter is observed to be a sinusoid of frequency $40$ Hz $.$ What is the frequency of the continuous$-$time sinusoid signal $\backslash ($ x$($t$)\backslash )?$