Shopkeepers devise several ways to attract customers. Sometimes they sell an article at a price lower than its list price (LP)/ marked price (MP). The reduction offered by retailer on the list price is called discount. Sometimes more than one discounts are offered by the shopkeeper on a single item or article. When two or more discounts are applicable successively to the list price of an article, they form the discount series. It may be noted that each subsequent successive discount is calculated on the price obtained after allowing the previous discount. First discount is applied on the list price/marked price.

Discount = marked price × rate of discount

Selling price = marked price – discount

Let us consider some examples to illustrate the above ideas.

Example 01:  The marked price of a shirt was Rs 165 and it was sold at a discount of 12%. Find the discount allowed on the shirt and also its selling price.

Example 02:  Marked price of a dining table is Rs. 1350. It is sold at Rs. 1188 after allowing certain discount. Find the rate of discount.

SUCCESSIVE DISCOUNTS: 

Suppose a shopkeeper is offering 3 successive discounts of 10%, 20% and 30% then to calculate effective discount we assume that marked price is 100, then final value becomes 0.90×0.80×0.70×100 = 50.4.

Total discount = 49.6%

This effective discount will change if we change the values of the three successive discounts. Suppose, the same discount is offered as 20%, 20% & 20% then final value would be 0.8×0.8×0.8×100 = 51.2 or effective discount = 48.8%.

We see here that effective discount is minimum when a discount percentage is divided into several small but equal discounts. For example, if we divide a discount of 60% into two discounts of 30% each, then the effective discount will be 51% only. If we further divide the discount as 20%, 20% & 20% then the effective discount will be reduced to 48.8%.

(1) 37 %, 11%, 12%
(2) 19 %, 21%, 20%
(3) 10%, 50%
(4) 5%, 50%, 5%

Example 04:  Find a single discount equivalent to a discount series 20%, 10% , 10%.