P$-$Tex. Limited has total annual sales $($all credit$)$ of Rs$.4,000,000$ and a gross profit margin of $20$ percent. Its current assets are Rs$.800,000$; current liabilities, Rs$.600,000$; inventories Rs$.300,000$; and cash Rs$.100,000.$

a$.$ How much average inventory should be carried if management wants the inventory turnover to be $4?$

b$.$ How rapidly $($in how many days$)$ must accounts receivable be collected if management wants to have an average of Rs$.500,000$ invested in receivables? $($Assume a $360-$day year$).$