Basic Arithmetic Formulas With Examples
Common Arithmetic Formulae with Solved Examples
Terminology Used in Percentages Calculation
The base is the whole in a problem. It is the standard used for comparison.
The amount is the part of the whole being compared to the base.
The rate is the ratio of the amount to the base. It is written as a percent.
Formula I - Calculating Amount
Amount = Base x Rate
Example: Charles sells his property for 420,000 (Base) and pays 5% commission (Rate) on the sale price. What is the amount of commission (Amount)?
Amount = 420,000 x 5%
Amount = 21,000
Formula II - Calculating Base
Base = Amount ÷ Rate
Example: A brokerage Mr.Jack gets 16,200 (Amount) commission on a sale which is 4.5% (Rate) of the sale price. What was the sale price (Base)?
Base = 16,200 - 4.5%
Base = 360,000
Formula III - Calculating Rate
Rate = Amount ÷ Base
Example A property was sold for 350,000 and the brokerage Mr.Jackson got 19,250 commission. What was the percentage of commission (Rate)?
Rate = 19,250 ÷ 350,000 x 100
Rate = 5.5%
Terminology Used in Interest, Principal, Time Calculation
Principal (P): The original sum of money loaned/deposited.
Interest (I): The amount of money that you pay/earn to borrow/deposit money.
Time (T): The duration for which the money is borrowed/deposited.
Rate of Interest (R): The percent of interest that you pay/earn for money borrowed/deposited
Formula IV - Calculating Interest
Interest = (Principal x Rate x Time) ÷ 100
ExampleWhat is the interest on 7500 at the rate of 12% per annum for 8 years?
Given P = 7500, T = 8 Years, R = 12%
Interest = (7500X12X8)/100
Interest = 7200
Formula V - Calculating Principal
Principal = 100 x ( Interest ÷ ( Rate x Time) )
Find the principal invested at 4% for 8 months if the interest is 20
Principal = 20 / (0.04 x 2/3)
Principal = 20/(0.08/3)
Principal = 750
Formula VI - Calculating Time
Time = 100 x ( Interest ÷ ( Principal x Rate ) )
Example: Mr. John deposit 350 into a bank account paying 1.2% simple interest per month. If John receiver 9 as interest, find the time for which the money stayed at the bank.
Given I = 9, P = 350, I = 14.4%
Time = 9 / (0.144 x 350)
Time = 0.1786 years
Time = 2 months and 5 days
Terminology Used in Profit and Loss Calculation
Cost price: Price at which an things is purchased.
Selling price: Price at which an things is sold.
Profit: If the selling price is more than the cost price, the difference between them is the profit incurred.
Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.
Discount: This is the reduction in price offered on the marked or listed price.
Formula VII - Calculating Profit
Profit = Selling Price - Cost Price
Example: Mr. Mike buys sugar at 20 per kg and sells it at 23 per kg. Find the Profit of Mr. Mike.
Profit = 23 - 20
Profit = 3
Formula VIII - Calculating Cost Price
Cost Price = Selling Price - Profit
Queen Jansi sold a pen for 24900 at a profit of 600. Find the price at which she bought it.
Selling Price = 24900, Profit = 600
Cost price = 24900 - 600
Cost price = 24300
Formula IX - Calculating Loss
Loss = Cost - Selling Price
Example:Mr Charles buys pencil at 20 and sells it at 18.how much Mr. Charles lost
Loss = 20 - 18
Loss = 2
Formula IX - Calculating Selling Price
Selling Price = Cost Price - Loss
Example:While selling of 10 pencil, A person incurred loss equal to cost price of 3 pencils. Find the selling price.
Selling Price = 10 - 3
Selling Price = 7
Formula X - Calculating Profit Percent
% Profit = Profit ÷ Selling Price
Example:Mr. Michael bought some toys at the rate of 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss percent.
Cost price of 10 toys = Rs. 40 -> CP of 1 toy = Rs. 4.
Selling price of 8 toys = Rs. 35 -> SP of 1 toy = Rs. 35/8
Therefore, Profit = 35/8 - 4 = 3/8.
% Profit = (3/8)/4 x 100 = 9.375%
% Profit = 9.4%
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Common Arithmetic Formulae with Solved Examples
Terminology Used in Percentages Calculation
The base is the whole in a problem. It is the standard used for comparison.
The amount is the part of the whole being compared to the base.
The rate is the ratio of the amount to the base. It is written as a percent.
Formula I - Calculating Amount
Amount = Base x Rate
Example: Charles sells his property for 420,000 (Base) and pays 5% commission (Rate) on the sale price. What is the amount of commission (Amount)?
Amount = 420,000 x 5%
Amount = 21,000
Formula II - Calculating Base
Base = Amount ÷ Rate
Example: A brokerage Mr.Jack gets 16,200 (Amount) commission on a sale which is 4.5% (Rate) of the sale price. What was the sale price (Base)?
Base = 16,200 - 4.5%
Base = 360,000
Formula III - Calculating Rate
Rate = Amount ÷ Base
Example A property was sold for 350,000 and the brokerage Mr.Jackson got 19,250 commission. What was the percentage of commission (Rate)?
Rate = 19,250 ÷ 350,000 x 100
Rate = 5.5%
Terminology Used in Interest, Principal, Time Calculation
Principal (P): The original sum of money loaned/deposited.
Interest (I): The amount of money that you pay/earn to borrow/deposit money.
Time (T): The duration for which the money is borrowed/deposited.
Rate of Interest (R): The percent of interest that you pay/earn for money borrowed/deposited
Formula IV - Calculating Interest
Interest = (Principal x Rate x Time) ÷ 100
ExampleWhat is the interest on 7500 at the rate of 12% per annum for 8 years?
Given P = 7500, T = 8 Years, R = 12%
Interest = (7500X12X8)/100
Interest = 7200
Formula V - Calculating Principal
Principal = 100 x ( Interest ÷ ( Rate x Time) )
Find the principal invested at 4% for 8 months if the interest is 20
Principal = 20 / (0.04 x 2/3)
Principal = 20/(0.08/3)
Principal = 750
Formula VI - Calculating Time
Time = 100 x ( Interest ÷ ( Principal x Rate ) )
Example: Mr. John deposit 350 into a bank account paying 1.2% simple interest per month. If John receiver 9 as interest, find the time for which the money stayed at the bank.
Given I = 9, P = 350, I = 14.4%
Time = 9 / (0.144 x 350)
Time = 0.1786 years
Time = 2 months and 5 days
Terminology Used in Profit and Loss Calculation
Cost price: Price at which an things is purchased.
Selling price: Price at which an things is sold.
Profit: If the selling price is more than the cost price, the difference between them is the profit incurred.
Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.
Discount: This is the reduction in price offered on the marked or listed price.
Formula VII - Calculating Profit
Profit = Selling Price - Cost Price
Example: Mr. Mike buys sugar at 20 per kg and sells it at 23 per kg. Find the Profit of Mr. Mike.
Profit = 23 - 20
Profit = 3
Formula VIII - Calculating Cost Price
Cost Price = Selling Price - Profit
Queen Jansi sold a pen for 24900 at a profit of 600. Find the price at which she bought it.
Selling Price = 24900, Profit = 600
Cost price = 24900 - 600
Cost price = 24300
Formula IX - Calculating Loss
Loss = Cost - Selling Price
Example:Mr Charles buys pencil at 20 and sells it at 18.how much Mr. Charles lost
Loss = 20 - 18
Loss = 2
Formula IX - Calculating Selling Price
Selling Price = Cost Price - Loss
Example:While selling of 10 pencil, A person incurred loss equal to cost price of 3 pencils. Find the selling price.
Selling Price = 10 - 3
Selling Price = 7
Formula X - Calculating Profit Percent
% Profit = Profit ÷ Selling Price
Example:Mr. Michael bought some toys at the rate of 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss percent.
Cost price of 10 toys = Rs. 40 -> CP of 1 toy = Rs. 4.
Selling price of 8 toys = Rs. 35 -> SP of 1 toy = Rs. 35/8
Therefore, Profit = 35/8 - 4 = 3/8.
% Profit = (3/8)/4 x 100 = 9.375%
% Profit = 9.4%
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