In discount we will learn how to solve problems related to marked price, list price and discount.

Marked Price:

In big shops and departmental stores, every article is tagged with a card and its price is written on it. This is called the **marked price** of that article, abbreviated as **MP**.

For books, the printed price is the marked price.

List Price:

Items which are manufactured in a factory are marked with a price according to the list supplied by the factory, at which the retailer is supposed to sell them. This price is known as the **list price** of the article.

In order to increase the sale or clear the old stock, sometimes the shopkeepers offer a certain percentage of rebate on the marked price. This rebate is known as **discount**.

**Notes: **

The discount is always reckoned on the marked price.

**As:**

**'selling price'** is the amount you actually pay for the thing when you purchase.

**'marked price'** is the general price of the thing without any discount.

**'discount'** is a percentage of the marked price.

**Worked-out problems related on discount, selling price and marked price based on the above formula are discussed below with a detailed explanation. **

**1.** The marked price of a ceiling fan is $ 1250 and the shopkeeper allows a discount of 6% on it. Find the selling price of the fan.

**Solution:**

Marked price = $ 1250 and discount = 6%. **Discount = 6% of Marked Price**

= (6% of $ 1250)

= $ {1250 × (6/100)}

= $ 75 **Selling price = (Marked Price) - (discount) **

= $ (1250 - 75)

= $ 1175.

Hence, the selling price of the fan is $ 1175.

**2.** A trader marks his goods at 40% above the cost price and allows a discount of 25%. What is his gain percent? **Solution:**

Let the cost price be $ 100.

Then, marked price = $ 140. **Discount = 25% of Marked Price **

= (25% of $ 140)

= $ {140 × (25/100)

= $ 35. **Selling price = (marked price) - (discount) **

= $ (140 - 35)

= $ 105.

Gain% = (105 - 100) % = 5%.

Hence, the trader gains 5%.

**3.** A dealer purchased a washing machine for $ 7660. He allows a discount of 12% on its marked price and still gains 10%. Find the marked price of the machine.

**Solution:**

Cost price of the machine = $ 7660, Gain% = 10%.

Therefore, selling price = [{(100 + gain%)/100} × CP]

= $ [{(100 + 10)/100} × 7660]

= $ [(110/100) × 7660]

= $ 8426.

Let the marked price be $ x.

Then, the discount = 12% of $x

= $ {x × (12/100)}

= $ 3x/25

Therefore, SP = (Marked Price) - (discount)

= $ (x - 3x/25)

= $ 22x/25.

But, the SP = $ 8426.

Therefore, 22x/25 = 8426

⇒ x = (8426 × 25/22)

⇒ x = 9575.

Hence, the marked price of the washing machine is $ 9575.

**4.** How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%?

**Solution:**

Let the cost price be $ 100.

Gain required = 20%.

Therefore, selling price = $ 120.

Let the marked price be $x.

Then, discount = 25% of $x

= $ (x × 25/100)

= $ x/4

Therefore, selling price = (Marked Price) - (discount)

= $ {x - (x/4)

= $ 3x/4

Therefore, 3x/4 = 120

⇔ x = {120 × (4/3)} = 160

Therefore, marked price = $ 160.

Hence, the marked price is 60% above cost price.

If two or more discounts are allowed one after the other then such discounts are known as **successive discounts** or discounts in series.

Suppose a discount of 25% is given on an article. Then on the reduced price a discount of 15% is given. In such a case, we say that successive discounts of 25% and 15% are given.

**5.** Find the single discount equivalent to two successive discounts of 20% and 10%.

**Solution:**

Let the marked price of an article be $ 100.

Then, first discount on it = $ 20.

Price after first discount = $ (100 - 20) = $ 80.

Second discount on it = 10% of $ 80

= $ {80 × (10/100)} = $ 8.

Price after second discount = $ (80 - 8) = $ 72.

Net selling price = $ 72.

Single discount equivalent to given successive discounts = (100 - 72)% = 28%.

● **Profit, Loss and Discount**

**Calculating Profit Percent and Loss Percent**

**Word Problems on Profit and Loss**

**Examples on Calculating Profit or Loss**

**Practice Test on Profit and Loss**

**Practice Test on Profit Loss and Discount**

● **Profit, Loss and Discount - Worksheets**

**Worksheet to Find Profit and Loss**

**Worksheets on Profit and Loss Percentage**

**Worksheet on Gain and Loss Percentage**

**8th Grade Math Practice**** ****From Discount to HOME PAGE**

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