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CHAPTER 6
MATHEMATICS OF SELLING
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6.1 Markup

In order to gain profit from selling, the
company must sell their product at a higher
price than the product cost.

The difference between a product’s cost and
selling price is refer to as markup.

It can be either in money value or
percentage.

The rate of mark-up is known as markup
percentage.
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Formula: Markup = Selling Price – Cost Price
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6.2 Markup Percent

Markup is usually expressed as a percent.

It can be expressed as:
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a) Markup percent based on retail price
% Mr = M x 100%
R
b) Markup percent based on cost price
% Mc = M x 100%
C
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Example 1:
The cost price of a piano is RM 4500. What is the
retail price if the seller wants a 15% mark-up
based on
a) Cost price, and
b) Retail price.
Solution:
a) R = C + M
R = RM 4500 + (RM 4500 x 15%)
R = RM 4500 + RM 675
R = RM 5175
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b) Let the retail price be X. Then
R=C+M
X = RM 4500 + 0.15X
X – 0.15X = RM 4500
0.85X = RM 4500
X = RM 4500
0.85
X = RM 5294.12
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Example 2:
ABC boutique purchases 100 dresses at a cost of
RM 18 each. The boutique expects that 20% of the
dresses will be sold at a reduced price of RM 12
each. If the boutique is to maintain a 65% mark-up
on cost on the entire purchase, find the regular
price of the dresses.
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Solution:
Cost of 100 dresses = RM 18 x 100 = RM 1800
Mark-up 65%
Sale of 100 dresses = RM 1800 x 0.65(RM 1800)
= RM 2970
Sale of 20 dresses = RM 12 x 20 = RM 240
Sale of remaining 80 dresses
= RM 2970 – RM 240
= RM 2730
Regular selling price = RM 2730 = RM 34.13 per
80
dress
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Example 3:
A retailer purchased 150 kg of tomato at RM 1.20
per kg. A 8% spoilage is expected. If he plans to
make a 55% mark-up based on overall cost, what
is the selling price of the tomato?
Solution:
Overall cost = RM 1.20 x 150 kg = RM 180
Amount left after deducting spoilage
= 150 kg – 0.08(150)
= 138 kg
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Mark-up 55%
R=C+M
= RM 180 + 0.55(RM 180)
= RM 279 (retail price for 138 kg)
Selling price per kg = RM 279
138
= RM 2.02
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6.3 Conversion of Markup Percent

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Markup percent based on retail price:
Since R = C + M
1 + % Mc = 100% + % Mc
Hence :
Markup percent based on retail price:
% Mc
% Mr 
1  % Mc
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
Markup percent based on cost price:
Since R = C + M
100% = 1 - % MR + % MR
Hence :
Markup percent based on cost price:
% Mr
% Mc 
1  % Mr
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Example :
a) The mark-up percent on cost price of an item is
20%. What is its mark-up percent based on
retail price?
b) The mark-up percent based on retail price of
an item is 15%. What is its mark-up percent
based on cost price?
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Solution:
a) % Mr = % Mc
1 + % Mc
= 0.2
1 + 0.2
= 0.1667 = 16.67%
b) % Mc = % MR
1 - % MR
= 0.15
1 - 0.15
= 0.1765 = 17.65%
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6.4 Markdown

Sometimes retailer may reduce the marked
price due to special promotions, festive
seasons or the items being obsolete.

Markdown is the reduction from the selling
price or marked price, normally in terms of
percentage.
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Formula:
Markdown Amount = Old Selling Price –
New Selling Price
Markdown percent based on old price,
% MD = MD x 100%
OP
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Example 1:
The markdown percent on a handphone is 15%. If
the new retail price is RM 850, find the old retail
price.
Solution:
Let the old price be RM K
% MD = MD x 100%
OP
0.15 = (K – 850)
K
0.15K = K – 850
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0.85 K = 850
K = 850
0.85
= RM 1000
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Example 2:
During the year end sales, a department store
marked down a pair of shoes by 25%, making the
selling price RM 270. At this selling price, the
department store made a 18% mark-up on the
selling price. Find
a) The regular price of the shoes.
b) The cost of the shoes.
c) The mark-up percent of the shoes at the
regular price.
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Solution:
a) NP = L (1 – r)
270 = L (1 – 0.25)
L = 270
0.75
= RM 360
b)
R=C+M
270 = X + 0.18(270)
X = 270 – 48.6
= RM 221.40
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c) Mark-up percent at regular price,
% Mr = M x 100%
R
= (Regular price – Cost) x 100%
Regular price
= (360 – 221.40) x 100%
360
= 38.5%
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6.5 Profit and Loss
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
Business does not always generate income
or profit.

If the business is not managed properly, it
may increase operating expense and
indirectly increase cost of the product.

The actual cost of the product is the
purchase price plus operating expenses.

In accounting, operating expenses include
cost of goods sold, official rental,
advertising, salary, commission and so on.
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
In general, there are three possibilities in
business:
a) M = OE
b) M > OE
c) M < OE
:
:
:
Break-even
Profit
Loss
Where:
M = Markup
OE = Operating Expenses
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−
Formula:
Break-even Price, BEP = Cost Price + OE
Retail Price = Cost + Net Profit + OE
Net Profit / (Loss) = Retail Price – BEP
Gross Profit = NP + OE
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Example :
A retailer bought a radio for RM 200. Buying
expenses amounted to RM 20. Operating
expenses incurred were 20% of the cost price. If
the retailer made a 25% net profit based on cost,
find
a) The retail price,
b) The gross profit ,
c) The net profit,
d) The breakeven price, and
e) The maximum markdown that could be offered
so that there is no profit or loss.
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Solution:
a) Retail price = 220 + 0.25(220) + 0.2(220)
= RM 319
b) Gross profit = NP + OE
= 0.25(220) + 0.2(220)
= RM 99
c) Net profit = Gross profit – OE
= 99 – 44
= RM 55
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d)
Breakeven price = C + OE
= 220 + 44
= RM 264
e)
Maximum reduction in price = R – BEP
= 319 – 264
= RM 55
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