Comparing Quantities 8 Mathematics — Revision Notes
Comparing quantities involves ratios, proportions, percentages, and their applications in practical situations. These tools help solve problems related to
TL;DR: Comparing quantities involves ratios, proportions, percentages, and their applications in practical situations. These tools help solve problems relate…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Comparing quantities involves ratios, proportions, percentages, and their applications in practical situations. These tools help solve problems related to
Key Points to Remember
- A ratio compares two quantities using division, expressed as a:b or a/b
- Equivalent ratios have the same value, like 2:3 and 4:6
- A proportion states that two ratios are equal, written as a:b = c:d or a/b = c/d
- Percentage is a ratio expressed out of 100, with the symbol %
- To convert a fraction to percentage: multiply by 100 and add %
- To convert a percentage to fraction: divide by 100
- Profit is selling price minus cost price when profit occurs
- Loss is cost price minus selling price when loss occurs
- Profit percentage = (Profit / Cost Price) × 100
- Discount is a reduction in price on the marked price
- Discount percentage = (Discount / Marked Price) × 100
- Simple interest = (Principal × Rate × Time) / 100
- Compound interest is calculated on principal plus accumulated interest, showing exponential growth
Important Formulas
- Ratio: a:b or a/b
- Percentage: (Part / Whole) × 100
- Profit Percentage: (Profit / Cost Price) × 100
- Loss Percentage: (Loss / Cost Price) × 100
- Discount: Marked Price - Selling Price
- Simple Interest: (P × R × T) / 100
- Compound Interest: A = P(1 + r/100)^n
Key Terms
- Ratio: Comparison of two quantities of the same kind using division
- Proportion: Statement that two ratios are equal
- Percentage: Ratio expressed as a number out of 100
- Profit: Amount gained when selling price exceeds cost price
- Discount: Reduction in price offered on the marked price of an item
- Simple Interest: Interest calculated only on the principal amount for a specified period
Frequently Asked Questions
How do you calculate profit percentage?
Profit percentage = (Profit / Cost Price) × 100. First find the profit by subtracting cost price from selling price, then divide by cost price and multiply by 100
What is the difference between discount and profit?
Discount is a reduction in marked price to get the selling price. Profit is the difference between selling price and cost price. An item can have a discount but still yield profit
Why is compound interest higher than simple interest?
Compound interest is calculated on principal plus accumulated interest each period, while simple interest is only on the original principal. This causes exponential growth in compound interest over time
More 8 Mathematics Revision Notes
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →