**Calculating Markups and Markdowns Worksheet :**

Worksheet given in this section will be much useful to the students who would like to practice solving word problems on profit, loss, percentage and discount.

Before look at the worksheet, if you would like to know basic stuff related to mark up and mark down,

**Problem 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 ?

**Problem 2 : **

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.

**Problem 3 : **

On selling 20 units of an item, the profit is equal to cost price of 5 units. Find the mark mark up rate.

**Problem 4 :**

Difference between the cost price of two products is $10. Difference between the selling price is $20. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

**Problem 5 : **

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

**Problem 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

**Problem 2 :**

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

**Problem 3 :**

On selling 20 units of an item, the profit is equal to cost price of 5 units. Find the mark mark up rate.

**Solution :**

Let m be the cost price of one unit.

Then, we have

Cost price of 5 units = 5m

Cost price of 20 units = 20m

**Given :** On selling 20 units of an item, the profit is equal to cost price of 5 units.

Then, we have

Profit on selling 20 units = C.P of 5 units = 5m

Mark up rate = (profit / cost) ⋅ 100%

Mark up rate = (5m / 20m) ⋅ 100%

Mark up rate = (1 / 4) ⋅ 100%

Mark up rate = 25%

**Problem 4 :**

Difference between the cost price of two products is $10. Difference between the selling price is $20. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

**Solution :**

Let x and y be the cost prices of two products.

Then, we have

x - y = 10 -----(1)

Let us assume that x is sold at 20% profit.

Then, the selling price of x is

= 120% ⋅ x

= 1.2x

Let us assume that y is sold at 20% loss.

Then, the selling price of y is

= 80% ⋅ y

= 0.8y

**Given :** Difference between the selling price is $20

1.2x - 0.8y = 20

Multiply each side by 10.

12x - 8y = 200

Divide each side by 4.

3x - 2y = 50 -----(2)

Solving (1) and (2), we get

x = 30

y = 20

So, the cost prices of the two products are $30 and $20.

**Problem 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 is $120.

Let x be the selling price.

From the above picture, we get

90% of (M.P) = x

(0.9) ⋅ 120 = x

108 = x

Therefore, the selling price is $108.

Cost price = $100

Selling Price = $108

Mark up rate = 8%

After having gone through the stuff given above, we hope that the students would have understood, how to solve mark up and mark down word problems.

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