Ratio and Proportion

1) Hook — A Fun Real-Life Example

Imagine you are at a famous cricket match, like India vs Australia at the Eden Gardens. The commentator says, "The ratio of runs scored by Virat Kohli to Rohit Sharma is 3:2." If Kohli scored 90 runs, how many runs did Rohit score? This is where understanding Ratio and Proportion helps you quickly find the answer and impress your friends!

2) Core Concepts — What are Ratio and Proportion?

Ratio compares two quantities showing how much of one thing there is compared to another. It is written as a : b or a/b.

Example: If a Bollywood movie has 6 songs sung by male singers and 4 songs by female singers, the ratio of male to female songs is 6 : 4, which simplifies to 3 : 2.

Proportion is an equation that states two ratios are equal. It helps us find unknown values.

Example: If 3 cups of sugar are needed for 5 cups of flour, how much sugar is needed for 10 cups of flour?

Set up the proportion:

3/5 = x/10

Cross multiply:

3 × 10 = 5 × x

So, 30 = 5x ⇒ x = 6 cups of sugar

3) Key Formulas / Rules

4) Did You Know?

In ancient India, mathematicians like Pingala used ratios in prosody (study of poetic meters) to arrange syllables in poetry — much like how Bollywood music directors arrange beats and rhythms!

5) Exam Tips

• Always simplify ratios before solving proportion problems to avoid mistakes.
• Use cross multiplication carefully; write the equation clearly to avoid confusion.
• Check units — if the question involves quantities like liters, kilograms, or rupees, keep units consistent.
• Board exam questions often ask for finding missing values in proportion or simplifying ratios. Practice these thoroughly.
• Common mistake: Mixing up the order of terms in ratios. Remember, a : b is NOT the same as b : a.