Yana and Ursula's Corporation $($traded as YUC on the NASDAQ$)$ have annual credit sales of $$255,000.$ Their credit terms are $\frac{2}{18},$ net $30.$ Additionally, $50\%$ of their customers take the discount and pay on day $18,$ and $50\%$ of their customers pay on day $30.($Assume a $360$ day year$)$

What is their Average Collection Period $($in days$)?$

$24$

$18$

$15$

not enough data provided

$30$