Ratio is a way to compare two or more quantities in a simple form. Ratios show how many times one number contains another. The formula for calculating ratio is: Ratio (a : b) = a ÷ b
Where:
- a = First quantity
- b = Second quantity
Ratio formula Quick 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 (CUET, SSC, Banking), real-life problems |
The ratio formula works by dividing one quantity by another to check their relationship. For example, if you have 20 apples and 10 oranges, the ratio of apples to oranges shows how many apples there are compared to oranges.
Steps:
- Write both quantities.
- Divide the first by the second.
- Simplify to the smallest whole numbers.
- Express it as a : b.
Ratios are used in mathematics exams (CUET, SSC, Banking, JEE) and in real life such as comparing marks, money, recipes, or business profits.
Examples to find Ratio
Example 1:
Find the ratio of 40 to 60.
Solution :
Step 1: Write as 40 : 60
Step 2: Divide both by their HCF (20).
Step 3: 40 ÷ 20 = 2,
60 ÷ 20 = 3
So , the ratio is 2 : 3
Example 2:
A student scored 45 marks in Maths and 30 in English. Find the ratio of marks.
Solution :
Step 1: Write as 45 : 30
Step 2: Divide by HCF (15).
Step 3: 45 ÷ 15 = 3,
30 ÷ 15 = 2
So , the ratio is 3 : 2
FAQs on Ratio Formula
Q1. Why do we simplify ratios?
Simplifying makes ratios easier to compare and understand, just like reducing fractions to the lowest terms.
Q2. Can ratios have decimals?
Yes, but they are usually written in whole numbers. For example, 2.5 : 5 becomes 1 : 2 after simplification.
Q3. Where is the ratio formula used in exams?
It appears in CUET, SSC, Banking, Railways, and JEE for word problems, data interpretation, and aptitude questions.
Q4. What is the difference between ratio and fraction?
A ratio compares two quantities (e.g., 2 : 3), while a fraction shows part of a whole (e.g., 2/3).
Q5. Can a ratio be written in percentage form?
Yes. A ratio like 1 : 4 can also be expressed as 25% (since 1 out of 4 is one-fourth = 25%).