F4: MATHEMATICS
NEW CHAPTER: Financial mathematics 1
1. Profit and Loss
Profit (P)
The amount gained by selling a product with more than its cost price.
Loss (L)
The amount the seller incurs after selling the product less than its cost price, is mentioned
as a loss.
Cost Price (CP)
The amount paid for a product or commodity to purchase it is called a cost price. Also,
denoted as CP. This cost price is further classified into two different categories:
Fixed Cost: The fixed cost is constant; it doesn’t vary under any circumstances
Variable Cost: It could vary depending as per the number of units
Selling Price (SP)
The amount for which the product is sold is called Selling Price. It is usually denoted as
SP. Also, sometimes called a sale price.
Profit or Gain = Selling price – Cost Price
Loss = Cost Price – Selling Price
The formula for the profit and loss percentage is:
Profit percentage = (Profit /Cost Price) x 100
Loss percentage = (Loss / Cost price) x 100
Example 1
A shopkeeper sold an article for Rs.60 which costs Rs.50 and another article sold for
Rs.110 which cost Rs.100. In each case, the shopkeeper makes a profit of Rs.10. It seems
that in both cases profit is equally gained.
But in percentage profit, we have:
Percentage Profit = 10/50 x 100% = 20%
Percentage Profit = 10/100 x 100% = 10%
Example 2:
A bag costing Rs.28 sold for Rs.35. Find the percentage profit.
BY HAADIPage 1
Solution:
Let Cost Price = Rs.28
Selling Price = Rs.35
Profit = Selling Price – Cost Price = 35 – 28 = Rs.7
Percentage Profit = 7/28 x 100% = 25%
Example 3 :
A machine costing Rs.60 sold for Rs.50. Find the percentage loss.
Solution:
Let Cost Price = Rs.60
Sold Price = Rs.50
Loss = Cost Price – Sold Price = 60 – 50 = Rs.10
Percentage Loss = 10/60 x 100% = 16.7%
Example 4: Suppose a shopkeeper has bought 1 kg of apples for sh.so100 . And sold
it for sh.so. 120 per kg.
a) How much is the profit gained by him?
Solution: Cost Price for apples is 100 sh.so.
Selling Price for apples is 120 sh.so.
Then profit gained by shopkeeper is ; P = SP – CP
P = 120 – 100 = sh.so. 20
b) Calculate the percentage of the profit gained by the shopkeeper.
Solution: We know, Profit percentage = (Profit /Cost Price) x 100
Therefore, Profit percentage = (20/100) x 100 = 20%.
Example 5: A man buys a fan for sh.so. 1000 and sells it at a loss of 15%. What is
the selling price of the fan?
Solution: Cost Price of the fan is sh.so.1000 Loss percentage is 15%
As we know, Loss percentage = (Loss/Cost Price) x 100
15 = (Loss/1000) x 100 Therefore, Loss = 150 sh.so.
So, Selling Price = Cost Price – Loss
= 1000 – 150
Selling Price = sh.so.850
EXERCISE
BY HAADIPage 2
1. A house was bought for $150 000 and later sold for $180 000. Calculate the
percentage profit.
2. A van, which cost $20 000, was later sold for $16 000. Find the percentage loss
2. DISCOUNT
Marked Price Formula (MP)
Discount = Marked Price – Selling Price
Discount Percentage = (Discount/Marked price) x 100
Example:
A watch priced at Rs.160 is sold for Rs.140. Find the percentage discount.
Solution:
Let Marked Price = Rs.160
Sale Price = Rs.140
Discount = Marked Price – Sale Price = 160 – 140 = Rs.20
Percentage Discount = 20/160 x 100 = 12.5%
Example:
The marked price of a washing machine is Rs.600. A discount of 6% is given during a
sale. What is the sale price of the washing machine?
Solution:
Let Marked Price = Rs.600
Discount Rate = 6%
Discount = 6% of the marked price = 6/100 x 600 = Rs.36
∴∴ Sale Price = Marked Price – Discount = 600 – 36 = Rs.564
EXERCISE
BY HAADIPage 3
1. An item of jewellery marked at $900 is discounted by 20% for cash payment.
Calculate
(i) The discount.
(ii) The price that a customer will pay when paying with cash
2. An article is marked at $ 40 and sold for $ 36. What percentage discount was
given?
3. Concept of Commission
A commission is the payment an agent gets for selling or buying something on
behalf of another person.
It is usually written as a percentage of the cost price or selling price.
Commission = commission rate x selling price
Example1 :
An agent got 2% commission for selling a plot for Rs.1000000. Find his commission.
Solution:
Let Sale Price = 1000000
Commission Rate = 2%
Amount of Commission = 2% x 1000000 = 2/100 x 1000000 = 20000
Example2:
An agent received Rs.6000 as commission for selling a house. If his commission rate is
2%, what is the selling price?
Solution:
Let Selling Price = x”
Commission Rate = 2%
Commission = (Selling Price)(Rate)
6000 = x x 2/100
x=300000
EXERCISE
BY HAADIPage 4
1. A car salesperson is paid 4% commission on the selling price of a vehicle. How
much will she receive if she sells a car for $20 000?
2. Amanda receives 5% on her first $5000 in sales and 10% on sales beyond $5000.
If her sales amounted to $13,000, what was her commission?
Calculating Simple Interest
In calculating Simple Interest, the principal remains constant over the period of the loan
and the amount of interest earned (or charged) remains the same each year. If the
principal, P is invested at a rate of R%, then the interest, I, for a period of one year will
be:
EXAMPLE 1
EXAMPLE 2
BY HAADIPage 5
EXERCISE
1. Find the interest on a boat loan of $5,000 at 16% for 8 months.
2. Find the total amount due on a loan of $600 at 16% interest at the end of 15
months.
BY HAADIPage 6
EXAMPLE 1
EXAMPLE 2
BY HAADIPage 7
BY HAADIPage 8
