# 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

**Example**What 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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