A single item EOQ model has been developed considering demand as a two parameter ramp type function and deterioration as a Heaviside’s function. Both pre and post deterioration discounts are considered where the former helps in maintaining constancy in the demand rate and the latter one boosts the demand of decreased quality items. The starting time periods of pre and post deterioration discount have been determined. The effect of both types of discounts in optimising the profit is examined through numerical illustrations. Sensitivity analysis is also appended to find out the effect of various system parameters. From this study it is observed that it will be more advantageous for management to offer pre deterioration discount in enticing the profit.