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.

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