Financial arithmetic Top presentation of today Profit and markup Department of education university of Sargodha

2. CONTENT
 Introduction
 Gain definition
 Profit
 Profit formula’s and example
 Markup
 Markup formula’s and example

3. GAIN:
We know that in a business, generally goods are bought at a certain
price and sold at a higher price. In such a case, there is a gain. What
is a Gain?
A gain, also called a capital gain, is an increase in the value of
an investment. It is the difference between the purchase price
(the basis) and the sale price of an asset. Thus the formula for gain
is:
Sale Price - Purchase Price = Gain
Note that this formula assumes the sale price is higher than the
purchase price. If an investor sells an asset for less than he or she
paid, this is called a loss.

4. EXAMPLE OF GAIN
Rida bought a watch set for RS.250 and sold for RS.350.Find the
gain?
Solution:
sale price= RS.350
cost price=RS.250
Gain= sale price – cost price
gain=350-250
Gain=RS.100

5. GAIN TERMS
While discussing this gain, we often use
two different terms.
1. Profit
2. Markup.

6. PROFIT:
“A profit means what we have earned after selling
a thing. It is calculated as a percentage of the
cost price.”
“Profit is the positive gain remaining for a
business after all costs and expenses have
been deducted from total sales. Profit is also
referred to as the bottom line, net profit or net
earnings.”

7. PROFIT AND PROFIT MARGIN FORMULA
The formula for profit is:
Sale price-cost price= Profit
Profit percentage:
Profit % = 100% × gain/Cost Price.

8. PROFIT PERCENTAGE:
Example: Hamza bought a jewelry set for Rs.84,000 and sold for Rs.855,00. Find the percentage of
profit.
Solution: Cost price (C.P) = Rs.84,000
Sale price (S.P) = Rs.85,500
Gain = Sale price - Cost price
= Rs.85,500 - Rs.84,000
= Rs. 1,500
Profit % = 100% × Gain/Cost Price
=(1500/84000*100)%
=1.79%

9. EXAMPLE: 1
The profit percentage on a bicycle is 40%. Find the
cost and sale profit of the bicycle when the
shopkeeper got a profit of Rs.500.
Solution: %Profit=40%
profit=Rs.500
cost price (C.P)=?
sale price( S.P)=?
%Profit= Profit/cost price*100%
40%=500/cost price*100%
40%/100%=500/cost price
4/10=500/cost price
4*C.P=500*10=5000
C.P=5000/4
C.P=Rs.1250
S.P=?
P=S.P-C.P
500=S.P-1250
500+1250=S.P
S.P=Rs.1750

10. EXAMPLES NO 1: A SHOPKEEPER BUYS PEN IN BULK FOR RS. 20 EACH. HE
SELLS THEM FOR 45 EACH. CALCULATE PROFIT AND PROFIT PERCENTAGE.
Cost price= Rs.20
Sale price: Rs.45
Profit= selling – cost
=45-20
=Rs. 25 so the profit is Rs. 25.
We know the formula of percentage as
Profit%=(profit/cost price *100)
=(25/20*100)
=1.25*100
Profit%=125%

11. EXAMPLE 2: USMAN BOUGHT A BIKE FOR RS. 135,000 AND SOLD AT 62% PROFIT.
FIND THE SALE PRICE OF THE BIKE.
Solution: Method I
% profit = 62%
Cost price = Rs.135,000
Sale price = ?
Sale price = (100% + 62%) x 135,000
rupees
= 162% x 135,000 rupees 162/100*
135 000
Rs. 218,700 100
Method II
%Profit= Profit/cost price*100
62=profit/ 135,000*100
Profit={62*135000/100}rupees
= Rs. 83,700
We know that;
Sale price = cost price + profit
= Rs.135,000 + Rs.83,700
= Rs.218,700

12. EXAMPLE 3: IMRAN SOLD A BICYCLE FOR RS. 3,978 AND GOT 17%
PROFIT. FIND THE COST PRICE OF THE BICYCLE.
Solution:
Sale price (S.P) = Rs.3,978
% Profit = 17%
By using formula,
Cost price(C.P)=Sale price /(100% + Profit%)
Cost price (C.P) = {3978 /117*100 }
=Rs. 3,400

13. EXAMPLE 4: ALI BOUGHT A SHIRT FOR 250 AND SOLD IT FOE RS. 295.
FIND THE PROFIT PERCENTAGE
Cost price(C.P)= RS.250
Sale price(S.P)=RS.295
Profit= sale price – cost price
=295-250
=45
%profit=profit/cost price*100%
=45/250*100%
=18%

14. MARKUP
 In our daily life, we often borrow money from our
friends and relatives to buy a thing that we repay them
after a certain period. Some banks and retail
organizations also provide the same services and charge
an additional amount called markup.
 Definition:
 “A markup is an amount added to a cost price to calculate
the sale price.”

15. MARKUP RATE AND PRINCIPLE
Markup rate:
we calculate the markup as a percentage of the actual amount paid
for a thing. This is called the markup rate.
Principle:
Paid amount itself is called the principal.

16. FORMULA:
Markup= sale price – cost price

20. MARKUP FORMULA PER ANNUM/AMOUNT OF MARKUP
Suppose “P” is the principal, “T” is the time
period and “R” is the markup rate, then the
amount of markup will be:
Markup = RPT/100

21. AMOUNT OF MARKUP EXAMPLE
Example: Aleem bought a television for Rs. 15,000 on installments at the markup rate of
12% per annum. Find the selling price of the television if time period is 3 years.
Solution: Cost price (P) = Rs. 15,000 ; Markup rate = 12% per annum
Time period (T) = 3 years ; Price of the Television = ?
Using the formula,
Amount of the markup= RPT/100
=12*15000*3/100
=Rs. 5 400
Price of the television = cost price + markup
= Rs. 15,000 + Rs. 5,400
= Rs. 20,400

22. EXAMPLE: MARKUP ON PRINCIPLE AMOUNT IS RS.820 FOR 6 MONTHS AT
THE RATE OF 12.5% PER ANNUM. CALCULATE THE PRINCIPLE AMOUNT
Markup= Rs 820
Markup rate (R)= 12.5%
Time period(T)=6 months
=6/12 years
=1/2 years
By using formula,
Markup=:RPT/100
820= 12.5*1/2*P
principal amount(p)= 820*100*2/12.5*1
= Rs.13120.

23. EXAMPLE 2:FIND THE MARKUP ON A THING WHOSE
PRICE IS RS. 45,000 FOR 73 DAYS AT THE RATE OF
10% PER ANNUM.
Solution: Principal (P) = Rs. 45,000
Markup rate (R) = 10% per annum,
Markup = ?
Time period = 73 days =365/73 =1/5
Using the formula,
Amount of the markup = RPT/100
=10*45000*1/5 /100
=10*45000*1 / 5*100
=Rs.900

24. 10 UNSOLVED QUESTION EXERCISES
1. Adnan bought 96 eggs at the rate of Rs.40 per dozen and sold at the rate
of Rs.4 per egg. Find the percentage of profit, if 3 eggs were rotten.
2. If 16% profit on a mobile set is Rs.832. Find the cost price of the mobile set.
3. Zia bought an out of order clock for Rs.750 and got it repaired for Rs.425.
What should be the selling price of the clock if Zia wants to earn 25%
profit?
4. Find the markup on a principal amount of Rs. 75,500 at the rate of 9% per
annum for 4 years.
5. Ujala bought a car for Rs.280,000 and spent Rs. 12,000 more on it. What
should be the selling price if she wants to get 7.5% profit?

25. 6. Khushi bought a computer for Rs. 100,000 and paid a markup of
Rs. 25,000 for 2 years. What markup rate did she pay?
7. The price of a bicycle including markup is Rs. 5610. If the
markup rate is 5% per annum, find the amount of markup for
146 days.
8. The markup on a principal amount is Rs. 820 for 6 months at the
rate of 12.5% per annum. Calculate the principal amount.
9. Find the markup on a thing whose price is Rs. 45,000 for 73 days
at the rate of 10% per annum.
10. Ada bought a jewelry set for Rs.84,000 and sold for Rs.855,00.
Find the percentage of profit.

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