# Successive Discounts

Before going on the topic (successive discount), let us first try to understand the concept of discount. While crossing a garment store on road, you must have come across the poster saying “Hurry, 20% off!!” in blocks. This percent written on the poster is the discount percent offered by the shopkeeper to their customers. It is actually some percentage off on the products so as to attract customers towards their products. Let us try to understand the actual situation of the market using an example. Let us suppose a case where a shopkeeper buys a t-shirt from a retailer at $500. He decides to sell it for$ 800. He then puts a discount of 20% on the t-shirt. After this discount the selling price of the t-shirt becomes:

= 800 - (20% of 800)

= 800 - (160)

= $640 If we look from the customer’s point of view we will find 20% off on the t-shirt. But from shopkeeper’s point, he is actually selling his product for$ 640 even after giving a discount of 20%, which he bought for $500. This means that the shopkeeper is having a profit of$ 140 even after the discount offered. This is what the actual situation of our market is.

Now let us move on to our main topic, i.e., successive discount. Successive discount is the discount offered on the discount. It is similar to compound interest (interest on interest). Let us have an example to understand the concept. Let the original price of a CD be ‘x’. a shopkeeper offers a discount of ‘y%’ and again ‘z%’ on the new price. What will be the selling price of the CD. The selling price of the CD can be calculated as:

Total discount can be calculated as: $$y+z-\frac{yz}{100}$$%

Now the selling price of the CD will be = $$x-(y+z-\frac{yz}{100})\times x$$.

Now let us solve some examples based upon the concept of successive discounts.

1. In a store the successive discounts offered on a bag are 10% and 20%. The store price of the bag is $570. Then calculate the selling price of the bag. Solution: Successive discounts offered on the bag = 10% and 20% Total discount offered on the bag = $$10+20-\frac{10 \times 20}{100}$$% = $$30-\frac{200}{100}$$% = 28% Discount = 28% of$570

= $$\frac{28}{100}\times 570$$

= $159.6 Selling price = store price – discount =$570 - $159.6 =$410.4

2. The store price of a t-shirt is Rs950. The successive discounts offered by the store is 30% and 50%. Calculate the total discount offered by the store. Also calculate the selling price of the t-shirt.

Solution:

successive discounts offered on the t-shirt = 30% & 50%

Total discount = $$30+50-\frac{30 \times 50}{100}$$%

= $$80-\frac{1500}{100}$$%

= 65%

Discount = 65% of Rs950

= $$\frac{65}{100}\times 950$$

= $617.5 Selling price =$ 950 – $617.5 =$ 332.5

Note: Now if three successive discounts are given as x%, y% and z% respectively and you need to calculate the total discount, then first calculate the total discount due to x% and y% using the above formula. Then calculate the overall discount using this total discount and z%.

3. The successive discounts on a product in a store is given as 5%, 10% and 15%. The store price of the product is $1000. Then calculate overall discount and selling price of the product. Solution: Successive discounts = 5%, 10% and 15%. Total discount due to 5% and 10% = $$5 + 10 - \frac{5\times 10}{100}$$% = $$15 - \frac{50}{100}$$% = 14.5% Overall discount due to 14.5% and 15% = $$14.5 + 15 - \frac{14.5\times 15}{100}$$% = $$29.5 - \frac{217.5}{100}$$% = 27.325% Discount = 27.325% of$ 1000

= $273.25 Selling price = store price – overall discount =$ 726.75

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