**Calculating Markups :**

A markup is one kind of percent increase. We can use a bar model to represent the retail price of an item, that is, the total price including the markup.

**Mark up ----> Increasing **

To get profit in a business, a trader increases the cost price and sells the product. This increment in price is called as "Mark up"

This "Mark up 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 markups", let us look at some examples.

**Example 1 : **

To make a profit, stores mark up the prices on the items they sell. A sports store buys skateboards from a supplier for s dollars. What is the retail price for skateboards that the manager buys for $35 and $56 after a 42% markup ?

**Solution : **

**Step 1 : **

Use a bar model.

Draw a bar for the cost of the skateboard S.

Then draw a bar that shows the markup: 42% of S, or 0.42S.

These bars together represent the cost plus the markup.

That is

S + 0.42S

**Step 2 :**

Retail price = Original cost + Markup

= S + 0.42S

= 1S + 0.42S

= 1.42S

**Step 3 : **

Use the expression to find the retail price of each skateboard.

S = $35 ----> Retail price = 1.42($35) = $49.70

S = $56 ----> Retail price = 1.42($56) = $79.52

**Example 2 : **

A computer store used a markup rate of 40%. Find the selling price of a computer game that cost the retailer $25.

**Solution : **

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

Here, M = 40, C.P = $25

Then, S.P = (100 + 40)% x 25

S.P = 140% x 25

S.P = 1.4 x 25 = $35

Hence, the selling price is $35.

**Example 3 : **

A golf store pays its wholesaler $40 for a certain club, and then sells it to a golfer for $75. What is the markup rate?

**Solution : **

Cost price (C.P) = $ 40

Selling price (S.P) = $ 75

Mark up value = 75 - 40 = $ 35

Mark up rate = (35/40)x100 % = 87.5 %

Hence, the mark up rate is 87.5 %

**Example 4 : **

A store uses a 40% markup on cost. Find the cost of a pair of shoes that sells for $63.

**Solution : **

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

Here, S.P = $ 63, M = 40

Plugging the above values in (1)

(1)-----------> 63 = (100+40)% x C.P

63 = 140% x C.P ---------> 63 = 1.4 x C.P

63/1.4 = C.P ---------> 45 = C.P

Hence, the cost of a pair of shoes is $ 45

**Example 5 : **

A trader cheats his customer to make a profit by stating that he sells at cost price but gives his customers only 800 grams. for every 1000 grams. What is the mark up rate?

**Solution :**

Cheated Value = 1000 - 800 = 200

False weight = 800

Mark up rate = (Cheated value/False weight)x100%

Mark up rate = (200/800)x100% = 25%

Hence, the mark up rate is 25 %

**Example 6 :**

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 7 :**

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 markups".

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