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.
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