**Worksheet on Markup and Markdown :**

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,

**Question 1 :**

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

**Question 2 :**

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

**Question 3 :**

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

**Question 4 :**

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?

**Question 5 :**

Mr. Lenin sold a chair at a loss of 15%. If he had sold at a mark up rate of 10%, he would have got $100 more. What is the cost price of the chair?

**Question 6 :**

I purchased 120 books at the rate of $3 each and sold 1/3 of them at the rate of $4 each. 1/2 of them at the rate of $ 5 each and rest at the cost price. Find my profit percentage.

**Question 7 :**

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

**Question 8 :**

A person buys 8 articles for $15 and sells them at 10 for $18. Find the gain or loss percentage.

**Question 9 :**

Sum of the cost price of two products is $50. Sum of the selling price of the same two products is $52. If one is sold at 20% and other one is sold at 20% loss, find the cost price of each product.

**Question 10 :**

On selling an item, a trader gets a profit of $20. If the selling price is five times the profit, find the mark up rate.

**Question 1 :**

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)% ⋅ C.P

Here,

M = 40, C.P = $25

Then,

S.P = (100 + 40)% ⋅ 25

S.P = 140% ⋅ 25

S.P = 1.4 ⋅ 25

S.P = $35

So, the selling price is $35.

**Question 2 :**

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)% ⋅ C.P -----(1)

Here,

S.P = $63, m = 40

Substitute 63 for S.P and 40 for m in (1).

(1)-----> 63 = (100 + 40)% ⋅ C.P

63 = 140% ⋅ C.P

63 = 1.4 ⋅ C.P

63 / 1.4 = C.P

45 = C.P

So, the cost of a pair of shoes is $45.

**Question 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) ⋅ 100%

Marked down rate = 25%

**Question 4 :**

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) ⋅ 100%

Mark up rate = (200 / 800) ⋅ 100%

Mark up rate = 25%

**Question 5 :**

Mr. Lenin sold a chair at a loss of 15%. If he had sold at a mark up rate of 10%, he would have got $100 more. What is the cost price of the chair?

**Solution :**

Let x be the cost price of the chair.

S.P (-15%) = 85% of x

S.P (-15%) = 0.85x -----(1)

S.P (+10%) = 110% of x

S.P (+10%) = 1.1x -----(2)

In (2), he got $100 more than (1).

Then, we have

(2) - (1) = 100

1.1x - 0.85x = 100

0.25x = 100

25x = 10000

x = 400

So, the cost price of the chair is $400.

**Question 6 :**

I purchased 120 books at the rate of $3 each and sold 1/3 of them at the rate of $4 each. 1/2 of them at the rate of $ 5 each and rest at the cost price. Find my profit percentage.

**Solution :**

Total money invested = 120 ⋅ 3 = $360 -----(1)

Let us see, how 120 books are sold in different prices.

From the above picture,

Total money received = 160 + 300 + 60 = $520 -----(2)

Profit = (2) - (1)

Profit = 520 - 360

Profit = $160

Mark up rate = (160 / 360) ⋅ 100%

Mark up rate = 44.44%

**Question 7 :**

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%

**Question 8 :**

A person buys 8 articles for $15 and sells them at 10 for $18. Find the gain or loss percentage.

**Solution :**

**Given : **A person buys 8 articles for $15 and sells them at 10 for $18.

Find the least common multiple of 8 and 10.

The least common multiple of 8 and 10 is 40.

Find both cost price and selling price for 40 articles.

**Cost price :**

8 articles -----> $15

40 articles = 5 ⋅ 8 articles = 5 ⋅ 15 = $75

C.P of 40 articles = $75 -----(1)

**Selling price :**

10 articles -----> $18

40 articles = 4 ⋅ 10 articles = 4(18) = $72

S.P of 40 articles = $72 -----(2)

From (1) and (2), the cost price is more than the selling price.

That is, C.P > S.P.

So, there is loss.

Loss = (1) - (2)

Loss = 75 - 72

Loss = 3

Loss percentage = (3 / 75) ⋅ 100%

Loss percentage = 4%

So, the loss percentage is 4.

**Question 9 :**

Sum of the cost price of two products is $50. Sum of the selling price of the same two products is $52. If one is sold at 20% 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 = 50 -----(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 :** Sum of the selling prices of x and y is $52.

Then, we have

1.2x + 0.8y = 52

Multiply each side 10.

12x + 8y = 520

Divide each side by 4.

3x + 2y = 130 -----(2)

Solving (1) and (2), we get .

x = 30

y = 20

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

**Question 10 :**

On selling an item, a trader gets a profit of $20. If the selling price is five times the profit, find the mark up rate.

**Solution :**

**Given :** Profit is $20 and selling price is five times the profit.

Then, we have

S.P = 5 ⋅ profit

S.P = 5 ⋅ 20

S.P = $100

C.P = S.P - Profit

C.P = 100 - 20

Therefore, the cost price is $80.

Mark up rate = (profit / cost) ⋅ 100%

Mark up rate = (20 / 80) ⋅ 100%

Mark up rate = (1 / 4) ⋅ 100%

Mark up rate = 25%

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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