Comparing Quantities

Comparing quantities involves determining the relationship between two or more quantities and expressing this relationship using mathematical formulas or concepts. This is an essential skill in various fields, such as finance, economics, and science. In this guide, we will discuss several formulas for comparing quantities and provide explanations and examples for each.

1. Ratio:
A ratio compares two quantities by dividing one quantity by the other. It is expressed as a fraction or using the colon symbol (:). The formula for ratio is:

Ratio = Quantity 1 / Quantity 2

Example: If there are 15 boys and 25 girls in a class, the ratio of boys to girls is 15:25 or 15/25.

2. Percentage:
Percentage is a way to express ratios or fractions as parts per hundred. It is often used to compare quantities in terms of their relative sizes. The formula for percentage is:

Percentage = (Part / Whole) * 100

Example: If 40 out of 100 students are girls, the percentage of girls in the class is (40/100) * 100 = 40%.

3. Profit and Loss:
Profit and loss are commonly used to compare the financial performance of a business. The formulas for profit and loss are:

Profit = Selling Price - Cost Price
Loss = Cost Price - Selling Price

Example: If an item is bought for $50 and sold for $70, the profit is $70 - $50 = $20.

4. Discount:
Discount is a reduction in price offered on a product or service. It is often expressed as a percentage. The formula for discount is:

Discount = Marked Price - Selling Price

Example: If an item is marked at $100 and sold for $80, the discount is $100 - $80 = $20.

5. Simple Interest:
Simple interest is a way to compare the amount of interest earned or paid on a principal amount over a specific period. The formula for simple interest is:

Simple Interest = (Principal * Rate * Time) / 100

Example: If the principal amount is $1000, the interest rate is 5% per annum, and the time period is 2 years, the simple interest is (1000 * 5 * 2) / 100 = $100.

Conclusion:
Comparing quantities involves using various formulas and concepts to determine the relationship between two or more quantities. The formulas discussed in this guide, such as ratio, percentage, profit and loss, discount, and simple interest, are fundamental tools for making comparisons in different contexts. Understanding and applying these formulas can help in making informed decisions and solving problems in real-life situations.