In this paper, an inventory model is studied with ramp type demand rate where holding cost is expressed as linearly increasing function of time. The study includes some features that are likely to be associated with certain types of inventory, like inventory of seasonal fruits and vegetables, newly launched fashion items, etc. When stock on hand is zero, the inventory manager offers a price discount to customers who are willing to backorder their demand. The optimum ordering policy and the optimum discount offered for each backorder are determined by minimizing the total cost in a replenishment interval.