**Calculating Markdowns :**

An example of a percent decrease is a discount, or markdown. A price after a markdown may be called a sale price. You can also use a bar model to represent the price of an item including the markdown.

**Mark Down ----> Decreasing**

To increase the sale, stores will decrease the price of a product by giving offer or discount. This offer or discount is called as "Mark down".

This mark down can either be in percent or in dollars.

To do mark up and mark down word problems answers, let us go through the hints related to "Markup and Mark down"

**Hint 1 :**

**Cost price and marked up percentage are given.**

**Cost price = C.P, Marked up percentage = M %**

**Then, Selling price (S.P) = (100+M)% x C.P**

**Hint 2 :**

**List price and marked down percentage are given.**

**List price = L.P, Marked down percentage = M %**

**Then, Selling price (S.P) = (100 - M)% x L.P**

**Hint 3 :**

**List price price and marked down value (in dollars ) are given. **

**List price = L.P, Marked down value = $M**

**Then, mark down rate = ( M / L.P ) x 100 %**

**Hint 4 :**

**Cost price and marked up value are given**

**Cost price = C.P, Marked up value = $M**

**Then, mark up rate = ( M / C.P ) x 100 % **

**Hint 5 :**

**Cost price and selling price are given. **

**Cost price = C.P, Selling price = S.P and S.P > C.P**

**So, Gain = S.P - C.P **

**Then, mark up rate = ( Gain / C.P ) x 100 %**

To have better understanding on "Calculating markdowns", let us look at some examples.

**Example 1 : **

A discount store marks down all of its holiday merchandise by 20% off the regular selling price. Find the discounted price of decorations that regularly sell for $16 and $23.

**Solution : **

**Step 1 : **

Use a bar model.

Draw a bar for the regular price P.

Then draw a bar that shows the discount: 20% of P, or 0.2P.

The difference between these two bars represents the price minus the discount.

That is,

P - 0.2P

**Step 2 :**

Sale price = Original price - Markdown

= p - 0.2p

= 1p - 0.2p

= 0.8p

**Step 3 :**

Use the expression to find the sale price of each decoration.

p = $16 ---> Sale price = 0.8($16) = $12.80

p = $23 ---> Sale price = 0.8($23) = $18.40

**Example 2 : **

A product is originally priced at $55 is marked 25% off. What is the sale price?

**Solution : **

Selling price (S.P) = (100 - M)% x L.P ---------(1)

Here, L.P = $ 55, M = 25

Plugging the above values in (1)

(1)-----------> S.P = (100 - 25)% x 55

S.P = 75% x 55 ---------> S.P = 0.75 x 55

S.P = 41.25

Hence, the selling price is $ 41.25

**Example 3 : **

A product that regularly sells for $425 is marked down to $318.75. What is the discount rate?

**Solution : **

Regular price = $ 425

Marked down price = $ 318.75

Marked down value = 425 - 318.75 = 106.25

Marked down rate = (106.25 / 425) x 100 %

Marked down rate = 25 %

Hence, the marked down rate is 25 %

**Example 4 : **

A product is marked down 15%; the sale price is $127.46. What was the original price?

**Solution : **

Selling price (S.P) = (100 - M)% x Original price ---------(1)

Here, S.P = 127.46, M = 15

Plugging the above values in (1), we get

127.46 = (100 - 15) x Original price

127.46 = 85% x Original price

127.46 = 0.85 x Original price

127.46 / 0.85 = Original price

149.95 = Original price

Hence, the original price is $ 149.95

**Example 5 :**

A trader marks his goods 20% above the cost price and allows a discount of 10% for cash. Find the mark up rate.

**Solution :**

Let the cost price be $100.

Then, marked price (M.P) = $120

Let the selling price be "X"

From the above picture, we get

90% of (M.P) = X

(0.9).120 = X

108 = X --------> S.P = 108

Cost price = $100, Selling Price = $108 ------> Mark up rate = 8 %

Hence, the mark up rate is 8%.

**Example 6 :**

A person wants to get 20% mark up rate after selling his object at 20% discount. Find the required percentage increase in marked price.

**Solution :**

Let the cost price be $100.

Then, the selling price = $120

Let the marked price be "X"

From the above picture, we get

80% of (M.P) = S.P

(0.8)X = 120

X = 150 --------> M.P = 150

Cost price = $100, Marked Price = $150

Hence, the required percentage increase = 50%

After having gone through the stuff given above, we hope that the students would have understood "Calculating markdowns".

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