A ratio is one of the simplest ways to compare two or more quantities. It shows how many times one number contains another. Ratios help us understand relationships between values in everyday life and mathematics. Whether comparing marks, money, height, or ingredients in a recipe, ratios make the comparison clear and meaningful. This concept is extremely important for exams like CUET, SSC, Banking, JEE, and school-level aptitude tests.
Ratio Formula Overview
| Part | Meaning | When it is Used |
|---|---|---|
| Formula | Ratio (a : b) = a ÷ b | To compare two numbers |
| a | First quantity | Marks, money, distance, etc. |
| b | Second quantity | Marks, money, distance, etc. |
| Use Case | Shows comparison | Exams & real-life calculations |
What is a Ratio?
A ratio is a mathematical way to compare two quantities by showing how many times one value contains the other. The formula Ratio (a : b) = a ÷ b helps measure the relationship between any two numbers. By dividing the first quantity by the second, we get a simplified comparison.
Ratios can be simplified further by dividing both values by their HCF (Highest Common Factor). This makes the ratio easier to understand and compare. Ratios are used in mark comparisons, recipes, business profits, investments, distances, and daily decision-making.
In mathematics and exams like CUET, SSC, Banking, and JEE, ratio-based questions are common because they test logical thinking and comparison skills.
Examples to Calculate Ratio
Example 1: Find the ratio of 40 to 60
Step 1: Write as 40 : 60
Step 2: Find HCF (20)
Step 3: 40 ÷ 20 = 2
60 ÷ 20 = 3
Final Ratio: 2 : 3
Example 2: Find the ratio of marks 45 (Maths) to 30 (English)
Step 1: Write as 45 : 30
Step 2: Find HCF (15)
Step 3: 45 ÷ 15 = 3
30 ÷ 15 = 2
Final Ratio: 3 : 2
FAQs about Ratio Formula
Q1. Why do we simplify ratios?
Simplifying makes ratios easier to compare and understand, similar to reducing fractions to simplest form.
Q2. Can ratios have decimals?
Yes, but they are mostly written in whole numbers after simplification, like 2.5 : 5 becomes 1 : 2.
Q3. Where is the ratio formula used in exams?
It appears in CUET, SSC, Banking, Railways, and JEE aptitude and data interpretation questions.
Q4. What is the difference between ratio and fraction?
A ratio compares two numbers (like 3 : 2), while a fraction shows part of a whole (3/2 or 1/2).
Q5. Can a ratio be written as a percentage?
Yes. For example, the ratio 1 : 4 can be written as 25% because 1 part out of 4 equals one-fourth or 25%.