In this section, we will learn, how to solve word problems on mark up and mark down.

First let us understand what is mark up and mark down.

**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.

**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.

**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)% ⋅ 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)% ⋅ 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) ⋅ 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) ⋅ 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) ⋅ 100%

**Hint 6 :**

Selling price and profit percentage are given.

How to find cost price ?

Use hint 1 and solve for C.P

**Hint 7 :**

Selling price and loss percentage are given.

How to find cost price ?

Use hint 2 and solve for C.P

**Hint 8 :**

Marked price : It is the price before discount given.

Selling price = Marked price - Discount value

**Hint 9 :**

Marked price = M.P, Discount percentage = D%

Then, the discount value is

= D% ⋅ M.P

Selling price is

= (100 - D)% ⋅ M.P

**Hint 10 :**

Marked price (M.P) and discount value are given.

Then the discount percentage is

= (Discount value / M.P) ⋅ 100%

**Hint 11 :**

Retailer using false weight :

A trader cheats his customer to make a profit by stating that he sells at cost price. But he gives his customer less than 1000 grams (false weight) for every 1 kilogram.

Then, the profit percentage is

= (Cheated value / False weight) ⋅ 100 %

Here,

Cheated value = Original weight - False weight

**Hint 12 :**

Two articles are sold at the same price. But, one is sold at a profit of p% and other one is sold at a loss of p%.

Then, the net result of the transaction is loss.

The loss percentage is

= (p^{2} / 100)%

**Hint 13 :**

The cost price of two articles is same. But, one is sold at a profit of p% and other one is sold at a loss of p%.

Then, the net result of the transaction is no profit and no loss.

**Example 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.

**Example 2 :**

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) ⋅ 100% = 87.5%

So, the mark up rate is 87.5 %

**Example 3 :**

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.

**Example 4 :**

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

**Solution : **

Selling price (S.P) = (100 - m)% ⋅ L.P -----(1)

Here,

L.P = $55, m = 25

Substitute 55 for L.P and 25 for m in (1).

(1)-----> S.P = (100 - 25)% ⋅ 55

S.P = 75% ⋅ 55

S.P = 0.75 ⋅ 55

S.P = 41.25

So, the selling price is $ 41.25.

**Example 5 :**

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%

**Example 6 :**

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

**Solution : **

Selling price (S.P) = (100 - m)% ⋅ Original price -----(1)

Here,

S.P = 127.46, m = 15

Substitute 127.46 for S.P and 15 for m in (1).

127.46 = (100 - 15)% ⋅ Original price

127.46 = 85% ⋅ Original price

127.46 = 0.85 ⋅ Original price

127.46 / 0.85 = Original price

149.95 = Original price

So, the original price is $ 149.95.

**Example 7 :**

A sells to B an item at 15% profit. B sells the same item to C at 20% profit. If C pays $ 1656 for it. What is the price at which A bought the item?

**Solution :**

Let x be the cost price of A.

Then, we have

Cost price of B = 1.15x

Cost price of C = 1.2(1.15x)

Cost price of C = 1.38x

**Given :** The cost of C is $1656.

1.38x = 1656

Divide each side by 1.38

x = 1200

So, the price at which A bought the item is $1200.

**Example 8 :**

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.

Do you need the shortcuts explained above as pdf document?

If you would like to have more practice problems on markup and markdown, please click on the links given below.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...