Differentiate the posterior probability over its percentage domain

In another National Eye Centre survey, p% are boys and the rest are girls. The probability a randomly chosen boy wears spectacles is 0.3, and for a randomly chosen girl it is 0.24.

(i) Find p if a randomly chosen child wears spectacles with probability 0.267.

(ii) For general p, let f(p) be the probability that a randomly chosen child who wears spectacles is a girl. Show that $f(p)=4(100-p)/(400+p)$. Prove by differentiation that f is decreasing for $0\le p\le100$, and explain the statement in context.