Comparing Quantities Formulas for Class 8

1. Ratio:
Ratio is a comparison of two or more quantities of the same kind. It is expressed in the form of a fraction or as a colon. The formulas related to ratio are:

- Ratio: Ratio of two quantities a and b is expressed as a:b or a/b.
- Equivalent Ratio: Two ratios a:b and c:d are equivalent if their cross products are equal, i.e., ad = bc.
- Compound Ratio: When ratios are multiplied or divided, it forms a compound ratio. For example, if a:b and c:d are two ratios, their compound ratio is (a * c):(b * d).

2. Proportion:
Proportion is a statement that two ratios are equal. It is expressed in the form of a:b = c:d. The formulas related to proportion are:

- Direct Proportion: Two quantities are said to be in direct proportion if an increase in one quantity leads to a corresponding increase in the other quantity. The formula for direct proportion is a/b = c/d.
- Inverse Proportion: Two quantities are said to be in inverse proportion if an increase in one quantity leads to a corresponding decrease in the other quantity. The formula for inverse proportion is a/b = d/c.

3. Percentage:
Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". The formulas related to percentage are:

- Percentage: Percentage is calculated as (Part/Whole) * 100.
- Percentage Increase: The formula to calculate percentage increase is ((New Value - Original Value) / Original Value) * 100.
- Percentage Decrease: The formula to calculate percentage decrease is ((Original Value - New Value) / Original Value) * 100.

4. Profit and Loss:
Profit and loss are terms used to describe the financial gain or loss made in a business transaction. The formulas related to profit and loss are:

- Profit: Profit is calculated as Selling Price - Cost Price.
- Loss: Loss is calculated as Cost Price - Selling Price.
- Profit Percentage: Profit percentage is calculated as (Profit / Cost Price) * 100.
- Loss Percentage: Loss percentage is calculated as (Loss / Cost Price) * 100.

5. Simple Interest:
Simple interest is the interest calculated on the principal amount for a specific period of time. The formulas related to simple interest are:

- Simple Interest: Simple interest is calculated as (Principal * Rate * Time) / 100.
- Principal: Principal is calculated as (Simple Interest * 100) / (Rate * Time).
- Rate: Rate is calculated as (Simple Interest * 100) / (Principal * Time).
- Time: Time is calculated as (Simple Interest * 100) / (Principal * Rate).

These are some of the important formulas for comparing quantities in Class 8. Understanding and applying these formulas will help in solving various