MARKUP AND MARKDOWN WORD PROBLEMS ANSWERS

Problem 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.

Problem 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 %

Problem 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.

Problem 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.

Problem 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%

Problem 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.

Problem 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. 

Problem 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.

Problem 9 :

In Tulsa, Oklahoma the sales tax is 7.9%. If you buy an $850 television in Tulsa, how much tax will you pay ?

Solution :

Price of television = $850

Sales tax = 7.9%

Sales tax means, we have to pay something extra. Then markup price will be 

(100 + 7.9)% of original price of the product

= 107.9% of 850

= 1.079(850)

= $917.15

So, the exact amount we should pay is $917.15.

Problem 10 :

The book Barn is having sale, All hardback books are 20% off, and all paperbacks are 10% off. Suppose you buy four paperbacks that originally cost $9 each and two hardbacks that originally cost $20. What percent of the total you have saved ? Round to the nearest percent ?

Solution :

Cost of hardback = $20

Cost of each paperback = $9

Cost of four paperback = 4x9 ==> 36

Amount spent without offer = 36 + 20

= $56

After discount, amount spent for hardback : 

= (100-20)% of 20

= 0.80 (20)

= 16

After discount, amount spent for paperpacks : 

= (100-10)% of 36

= 0.90 (36)

= 32.4

Percentage change = [(Old value - new value)/old value] x 100%

= [(56 - (32.4 + 16)) / 56] x 100%

= (7.6 / 56) x 100%

= 0.135 x 100%

= 13.5%

About 13%.

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

Worksheet 1

Worksheet 2

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