Learning Objectives
- Convert ratios to percentages and vice versa
- Find percentage increase or decrease
- Solve problems on profit, loss, and discount
- Calculate simple interest
Key Concepts
Ratio and Proportion
A ratio compares two quantities. Example: 3:5 means for every 3 of one, there are 5 of the other.
Two ratios are in proportion if they are equal: a/b = c/d
Percentage
Percentage means "per hundred."
To convert fraction to percentage: multiply by 100
To convert percentage to fraction: divide by 100
Percentage change = (Change / Original) × 100
Profit and Loss
Profit = Selling Price (SP) - Cost Price (CP) (when SP > CP)
Loss = Cost Price (CP) - Selling Price (SP) (when CP > SP)
Profit % = (Profit / CP) × 100
Loss % = (Loss / CP) × 100
Simple Interest
SI = (P × R × T) / 100
Where P = Principal, R = Rate per annum, T = Time in years
Amount = Principal + Simple Interest
Summary
Comparing quantities involves ratios, percentages, profit/loss, and interest. Percentages help compare quantities with different bases. Simple interest is calculated on the original principal. These concepts are widely used in daily life for shopping, banking, and business.
Important Terms
- Cost Price (CP)
- The price at which an article is bought
- Selling Price (SP)
- The price at which an article is sold
- Discount
- A reduction on the marked price
- Principal
- The original amount of money borrowed or invested
- Simple Interest
- Interest calculated only on the original principal amount
Quick Revision
- Percentage = (Value / Total) × 100
- Profit = SP - CP; Loss = CP - SP
- Profit% and Loss% are always calculated on CP
- Discount is always calculated on Marked Price (MRP)
- SI = PRT/100; Amount = P + SI
Practice Tips
- Calculate discounts while shopping to practice percentage problems
- Compare prices of items using ratios
- Calculate simple interest on fixed deposits or savings accounts