Comparing Quantities

1) Hook — A Fun Real-Life Story to Grab Attention

Imagine you are at a cricket match watching your favourite team, India, play against Australia. Virat Kohli scored 75 runs in 60 balls, while Steve Smith scored 90 runs in 80 balls. Who scored more efficiently? How can we compare their performances fairly? This is where Comparing Quantities comes in handy! Just like cricket stats, comparing quantities helps us understand which value is greater, smaller, or how much one quantity changes compared to another.

2) Core Concepts — Clear Explanation with Examples and Visual Tables

What does Comparing Quantities mean?

Comparing quantities means finding out how much one quantity is in relation to another. It helps us answer questions like:

• Is one quantity greater or smaller than the other?
• By how much does one quantity increase or decrease compared to the other?
• What is the ratio or percentage difference between two quantities?

Types of Comparisons:

• Difference: How much more or less one quantity is than another.
• Ratio: The relative size of two quantities expressed as a fraction or colon (:).
• Percentage: Comparison expressed out of 100.

Example 1: Comparing Heights of Bollywood Stars

Question: Who is taller and by how many centimetres?

Solution: Ranveer Singh is taller. Difference = 178 cm − 175 cm = 3 cm.

Example 2: Comparing Prices of Mangoes in Two Markets

Question: What is the percentage increase in price from the Local Market to the Supermarket?

Solution:

Difference = 100 − 80 = ₹20

Percentage increase = (Difference ÷ Original price) × 100 = (20 ÷ 80) × 100 = 25%

3) Key Formulas/Rules

4) Did You Know?

In cricket, the strike rate is a way of comparing how quickly a batsman scores runs. It is calculated as:

This is a perfect example of comparing quantities to understand performance better. For example, a strike rate of 150 means the batsman scores 150 runs per 100 balls, which is very fast!

5) Exam Tips — Common Mistakes and Board Exam Patterns

• Always identify the original quantity before calculating percentage change. Using the wrong original quantity leads to wrong answers.
• Pay attention to units. For example, don’t subtract kilograms from grams without converting them first.
• Remember the difference formula is always Larger − Smaller.
• Ratio questions often appear in word problems involving sharing or comparing amounts. Write the ratio in simplest form.
• Board exams may ask you to find: difference, ratio, percentage increase/decrease, or solve real-life problems involving these concepts.
• Practice solving problems with Indian contexts like prices of fruits, cricket scores, Bollywood stats, or school attendance.

Final tip: Always show your steps clearly in the exam to get full marks!