Ratios and Proportion

1) Hook — A Fun Real-Life Example

Imagine you are at a cricket match in Mumbai. The vendor sells 2 samosas for every 3 cups of chai. If you want to buy 6 samosas, how many cups of chai should you get to keep the same ratio?

This is exactly what ratios and proportions help us solve — comparing quantities and scaling them up or down while keeping their relationship the same!

2) Core Concepts — Understanding Ratios and Proportions

What is a Ratio?

A ratio compares two or more quantities of the same kind. It tells us how much of one thing there is compared to another.

For example, if a Bollywood dance troupe has 4 boys and 6 girls, the ratio of boys to girls is:

We write this ratio as 4 : 6. It can be simplified by dividing both numbers by 2:

4 : 6 = 2 : 3

What is Proportion?

A proportion states that two ratios are equal. It helps us find missing values when quantities change but keep the same ratio.

For example, if the ratio of sugar to flour in a recipe is 1 : 4, and you have 3 cups of sugar, how much flour do you need?

Since the ratios are equal, we write:

1/4 = 3/x

Cross multiply: 1 × x = 4 × 3 → x = 12

So, you need 12 cups of flour.

3) Key Formulas / Rules

4) Did You Know?

In cricket, the ratio of runs scored by two players often decides the match's momentum. For example, if Virat Kohli scores 75 runs and Rohit Sharma scores 100 runs, the ratio of their scores is 75 : 100 or 3 : 4. Coaches use such ratios to plan batting orders and strategies!

5) Exam Tips

• Always simplify ratios by dividing both terms by their greatest common divisor (GCD).
• Check units: Ratios compare quantities of the same kind (like apples to apples).
• Use cross multiplication carefully: Write proportions clearly before multiplying.
• Watch for trick questions: Sometimes ratios are given in fractions or decimals—convert them properly.
• Practice word problems: Many exam questions ask you to find missing quantities using proportions.