**Business Mathematics: Definition, Formulas & Applications**

Business mathematics are mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.

Business mathematics consists of mathematical concepts related to business. It mainly consists of profits, losses and interest. Mathematics is the foundation of any business. Business math financial equations, measurements that help in calculating profit and loss, interest rates, tax calculations, and payroll calculations, helping to finish business tasks effectively and efficiently.

Mathematics typically used in commerce includes elementary arithmetic, elementary algebra, statistics and probability. For some management problems, more advanced mathematics – such as calculus, matrix algebra and linear programming – is applied.

Business mathematics is closely related to the concepts of statistics that provide solutions to business problems. In business, we deal with the exchange of money or products that have a monetary value. Every action leads to some profit and some loss. To determine these factors we have to study the basic topics of mathematics like formulas to find profit, loss, percentages, discount, etc. Although the requirements for this subject do not contain pure mathematics, it does require mathematical reasoning and some math formulas. Here, we will discuss what business mathematics and important terms and formulas are with problems and solutions.

**What is business mathematics?**

Business Math always deals with profit or loss. The cost of the product is fixed by taking into account profit, margin, cash discount, trade discount, etc. Businesses use business mathematics to record and manage businesses. Business firms use mathematics in the departments of accounting, inventory management, marketing, sales forecasting, and financial analysis.

**Business Math Topics**

The most important topics covered in business mathematics are:

>Profit and loss

>Statistics

>Simple and compound benefit

>Interest rates

>Loans

>Price Margins and Write-offs Annotations

>Tax and tax laws

>Discount factor

>Annuities

>Insurance

>Attributed to him

>Consumption

>future and present values

>Financial Statements

**Basic Terms in Business Mathematics**

**Selling Price:** The market price for selling the product is taken.

**Cost price:** The original price of the product is the cost price.

**Profit:** If the selling price is greater than the cost price, the difference in prices is profit.

**Loss:** If the selling price is less than the cost price, the difference in prices is the loss.

**Discount:** The amount reduced in the selling price of the product.

**Simple Interest:** Simple interest is that interest which is charged against the amount of principal or part of the principal amount which is still unpaid.

**Compound interest:** Compound interest is the rate of investment that increases exponentially.

**Business Math Formulas**

Here, the nine basic formulas in business mathematics that we can’t ignore. They are:

**net income formula:**

Net Income = Revenue – Expenses

**Accounting equation:**

Assets = Liabilities + Equity

Equity = Assets – Liabilities

**Cost of Goods Sold Formula:**

COGS = Beginning inventory + Purchase during the period – Closing inventory

**break-even point formula:**

Break-even point = fixed cost / (sales price per unit – variable cost per unit)

**Current Ratio Formula:**

Current Ratio = Current Assets / Current Liabilities

**Profit Margin Formula:**

Profit Margin = (Net Income / Revenue) x 100

**Return on Investment (ROI) Formula:**

ROI = [(Investment Gain – Cost of Investment) / Cost of Investment] x 100

**Coding format:**

Coding Ratio = [(Revenue- COGS) / COGS] x 100

Selling Price Using Markup = (COGS x Percentage of Brands) + COGS

where,

COGS = cost of goods sold

**Inventory Shrinkage Formula:**

Inventory Shrinkage = [(Recorded Stock – Actual Stock) / Recorded Stock] x 100

Business Math Example

While doing business, one can earn good profit or face loss. The price of the product is determined, considering cost price, profit, margin, trade discount, cash discount, etc. The quoted price on the good is called the fixed price or catalog price. For business purposes, the manufacturer suggests a discount on MRP to the buyer. This is called a trade discount. In addition to the trade discount, if the buyer pays cash for the goods, he will get another discount called cash discount. The price of the object after subtracting the trade discount and the cash discount is called the selling price. Thus, we have selling price = cost price – discounts. Let’s discuss the most important concept called “profit and loss” here.

**Profit and Loss:**

Profit is the amount earned by the company when selling a product while loss is the amount less than the actual price of the product. The profit and loss equation is given based on the selling price and cost price of the commodity.

Profit = Selling Price – Cost Price = S.P. – C.P. (S.P. > C.P.)

Loss = Cost Price – Selling Price = C.P. – S.P. (CP > S.P.)

Both of these scales have percentage value as well and are given by;

Profit % = [(S.P. – CP) / CP]. x 100 = (Profit/CP) x 100

Loss % = [(CP – S.P.) / CP] x 100 = (Loss / CP) x 100

Business Mathematics Problems and Solutions

Question 1: A music system was bought for Rs.10,500 and sold at Rs.9,500. Find the amount of profit or loss.

Solution: Given,

Cost Price of the music system = Rs.10,500

Selling Price of the music system = Rs. 9,500

We can see here, C.P. is greater than S.P. Therefore, there is a loss in this business.

Hence, we need to calculate the loss amount.

Loss = C.P. – S.P.

Loss = 10,500 – 9,500 = Rs.1,000/-.

Question 2: A pair of shoes is bought at Rs 200 and sold at a profit of 10%. Find the selling price of the shoes.

Solution: Given,

Profit = 10% of Rs.200

P = (10/100) × 200 = Rs. 20

S.P. = C.P. + Profit

S.P. = 200 + 20 = Rs.220/-

Question 3: If the cost price of an article including 20% for taxes is Rs. 186, then find the original cost of the article excluding taxes.

Solution:

Let x be the original price of an article.

Tax = 20% of x = (20/100) × x = 0.2x

According to the given statement,

Original cost + tax = New cost price

x + 0.2x = Rs. 186

1.2x = Rs. 186

x = Rs. 186/1.2

x = Rs. 155

Therefore, the cost of the article without taxes = Rs. 155

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