  In [ PRL, 102, 010401 (2009)], Spekkens et al., have shown that quantum
preparation contextuality can power the parity-oblivious multiplexing (POM)
task. The bound on the optimal success probability of $n$-bit POM task
performed with the classical resources was shown to be the \textit{same} as in
a preparation non-contextual theory. This non-contextual bound is violated if
the task is performed with quantum resources. While in $2$-bit POM task the
optimal quantum success probability is achieved, in 3-bit case optimality was
left as an open question. In this paper, we show that the quantum success
probability of a $n$-bit POM task is solely dependent on a suitable
$2^{n-1}\times n$ Bell's inequality and optimal violation of it optimizes the
success probability of the said POM task. Further, we discuss how the degree of
quantum preparation contextuality restricts the amount of quantum violations of
Bell's inequalities, and consequently the success probability of a POM task.
