The document discusses percentages, discounts, and commissions. It provides examples of calculating percentages, discounts on prices, and commissions earned by salespeople. Percentages are calculated by taking a number's percentage of the total. Discounts are calculated by taking a percentage off the original or stated price. Commission is a percentage of the total sale price paid to the salesperson. Examples show how to calculate discounted prices, original prices given a discount amount, commission amounts, and total sales values.

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2. BY: ASSOCIATE PROFESSOR NADEEM UDDIN
Percentage
A percentage is a ratio or fraction whose denominator is 100.
Example-20
What is 40% of Rs.150.
Solution:
40
40% of 150 = 150 Rs.60
100
 =
Example-21
Find the sum of money of which Rs.60 is 40%.
Solution:
40% of x = 60
40
x 60
100
100
x 60 Rs.150
40
 =
=  =
Example-22
What percentage of Rs.150 is Rs.60
Solution:
x of 150 = 60
x
150 60
100
100
x 60
150

 =
= 
x = 40%

3. Example-23
A purchaser received a discount of 10% on the selling price of a mobile. If he paid
Rs.4500, what was the selling price of the mobile?
Solution:
Let x be the selling price
Paid percentage is 90%
Paid amount is 4500
90% of 4500=x
4500
100
90
= x
90
100
4500=x
x = Rs. 5000
Example-24
What was the Abu-Tarique’s income last year if he paid an income tax of
Rs.30,000 which is 5% of his income?
Solution:
Let x be the income
5% of x = 30000
30000
100
5
= x
5
100
30000=x
=x Rs.60000 per year.

4. Example-25
The assets of a person increased from Rs.150,000 to Rs.350,000. What was the rate
of change?
Solution:
Original Amount = Rs.150,000
New Amount = Rs.350,000
Amount of Change = 350000 – 150000
= 200000
100
AmountOriginal
ChangeofAmount
ChangeofRate =
= 100
150000
200000

= 133.33%
Use of percentage in business
Discount:
Reduction in stated price of an item from seller.
SP = Stated price
AD = Amount of discount
DR = Discout rate
DP = Discounted price
Where
DP = SP – AD
Or
DP = SP ( 1 – DR )
DR =
𝐴𝐷
𝑆𝑃
∗ 100

5. Example-26
The price of a chair is Rs. 1000,find the discounted price if the discount rate is 5%.
Solution:
Given information
SP = Rs. 1000
DR = 5% = 0.05
DP = ?
DP = SP ( 1 – DR )
DP = 1000 ( 1 – 0.05 )
DP = 1000 ( 0.95 )
DP = Rs.9 5 0
Example-27
The price of a chair is Rs.1000 is available at discount of Rs.50 ,find the
discounted price and the discount rate .
Solution:
Given information
SP = Rs. 1000
AD = Rs.50
DP = ?
DR = ?
DP = SP – AD
DP = 1000 – 50
DP = Rs.9 5 0
Now find
DR =
𝐴𝐷
𝑆𝑃
∗ 100
DR =
50
1000
∗ 100
DR = 5%

6. Example-28
A customer received a discount of 5% on the book value of a chair and paid
Rs.950,What was the book value of the chair.
Solution:
Given information
SP = ?
DP = Rs 950
DR = 5% = 0.05
SP =
𝐷𝑃
( 1−𝐷𝑅 )
SP =
950
( 1−0.05 )
SP =
950
0.95
SP = Rs.1000
Example-29
The market price of a chair is Rs.1000 if the customer got two consecutive
discount 5% and an additional discount 4%. Find the final value (Discounted
price).
Solution:
Given information
SP = 1000
DR1 = 5% = 0.05
DR2 = 4% = 0.04
DP = SP ( 1 - DR1 ) ( 1 - DR2 )
DP = 1000 ( 1 – 0.05 ) ( 1 – 0.04 )
DP = 1000 ( 0.95 ) ( 0.96 )
DP = Rs.912

7. DO YOURSELF
Q.1 An item with price of Rs.2000 is available at 12% discount.Find the
discounted price and amount of discount.( Ans: DP = 1760 and AD = 240)
Q.2 A shopkeeper gave 7
1
2
% discount to customer on a mobile, if the customer
paid Rs.32375 for this mobile.Find the face value of the mobile.(Ans:3500
Q.3 A mobile shopkeeper offered 7.5% discount to a customer,find the
discounted price and actual price of the mobile if the discount allowed was
Rs.2625.(Ans: DP = 32375 and Actual price = 35000)
Commission
Commission is a sum of money paid to a salesperson for every sale that he makes.
Example-30
A property agent sold a plot in Karachi for Rs5000000 and received 2%
commission.Find agent`s commission.
Solution:
Agent`s commission = 2% of 5000000
Agent`s commission = 0.02 × 5000000
Agent`s commission = Rs.100000

8. Example-31
At 2% rate of commission a sales agent got Rs.300000 on the sales of the plots if
the price of a plot is 5000000.Find the value of his sales and the number of plots he
sold.
Solution:
Given information
The price of a plot = Rs 5000000
Commission rate = 2% = 0.02
Commission on one plot = 0.02 × 5000000
Commission on one plot = Rs. 100000
Number of plots sold =
𝑇𝑜𝑡𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛
𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑜𝑛 𝑜𝑛𝑒 𝑝𝑙𝑜𝑡
Number of plots sold =
300000
100000
Number of plots sold = 3 plots
Total value of his sales = 3 × 5000000
Total value of his sales = Rs.15000000
Example-32
An agent received Rs.100000 for selling a plot,his rate of commission was
2%.What was the selling price?
Solution:
Given information
Commission = Rs 100000
Commission rate = 2% = 0.02
Commission = Commission rate × Selling price
100000 = 0.02 × Selling price
Selling price =
100000
0.02
Selling price = Rs.5000000

9. DO YOURSELF
Q.1 How much does a property dealer receive commission on a property of
worth Rs.2000000 at 1.5 % . (Ans: Rs.30000)
Q.2 At 1.5% rate of commission a property dealer got Rs. 150000 on the sales of
the properties if the price of a property is 20,00000.Find the value of his
sales and the number of properties he sold?
(Total value = 100,00000 and Number of plots = 5)