🔢 Percentages
Percentage means "out of 100" (per hundred)
▶ Play Door 20Percentage Calculations and Profit & Loss
What is Percentage?
Percentage means "per hundred" (from Latin "per centum"). A percentage is a fraction with denominator 100. The symbol % represents "out of 100".
Key Conversions:
Convert FromToMethodExample
FractionPercentageMultiply by 100%\(3/4 = 0.75 × 100% = 75%\)
PercentageFractionDivide by 100%\(40% = 40/100 = 2/5\)
DecimalPercentageMultiply by 100%\(0.65 × 100% = 65%\)
PercentageDecimalDivide by 100\(25% = 25 ÷ 100 = 0.25\)
Percentage of a Quantity:
To find \(x%\) of a quantity \(Q\), calculate: \(x/100 × Q\)
Example: 20% of 250 = \(20/100 × 250 = 0.2 × 250 = 50\)
What is Profit and Loss?
In business, items are bought at Cost Price (CP) and sold at Selling Price (SP).
• Profit occurs when SP > CP
• Loss occurs when SP Important Formulas:
ConceptFormula
ProfitSP - CP
LossCP - SP
Profit Percentage\(ProfitCP × 100%\)
Loss Percentage\(LossCP × 100%\)…
Worked example
Problem: Convert \(3/8\) to a percentage. Also, find 35% of 240.
- Step 1: Fraction to percentage: Multiply by 100%
- Step 2: \(3/8 × 100% = 300/8% = 37.5%\)
- Step 3: 35% of 240 = \(35/100 × 240\)
- Step 4: \(= 0.35 × 240 = 84\)
Answer: Step 4: \(= 0.35 × 240 = 84\)
Discount and Simple Interest
What is Discount?
Discount is a reduction in the selling price of an item. It is usually expressed as a percentage of the Marked Price (MP) or List Price.
Important Terms:
• Marked Price (MP): The original price printed on the item
• Discount: The amount subtracted from MP
• Selling Price (SP): The actual price paid after discount
Formulas:
ConceptFormula
Discount AmountMP × \(Discount%100\)
Selling Price after DiscountMP - Discount = MP × \((1 - Discount%100)\)
Discount Percentage\(DiscountMP × 100%\)
What is Simple Interest?
Simple Interest (SI) is the extra money paid for borrowing money or earned on savings. It is calculated only on the original principal amount.
Key Terms:
• Principal (P): The initial amount borrowed or invested
• Rate (R): Interest rate per year (as percentage)
• Time (T): Time period in years
• Simple Interest (SI): Interest…
Worked example
Problem: A shop offers a 15% discount on a ₹1200 watch. Find the discount amount and the selling price.
- Step 1: Discount = 15% of MP = \(15/100 × 1200\)
- Step 2: Discount = \(0.15 × 1200 = ₹180\)
- Step 3: SP = MP - Discount = \(1200 - 180 = ₹1020\)
Answer: Step 3: SP = MP - Discount = \(1200 - 180 = ₹1020\)
Tax Calculations and Financial Literacy
What is Tax?
Tax is a compulsory payment to the government on income, goods, or services. Understanding taxes helps in financial planning and literacy.
Common Types of Taxes:
Tax TypeDescriptionApplied On
GST (Goods and Services Tax)Tax on buying goods and servicesSelling price
Income TaxTax on money earnedAnnual income
Sales TaxOld tax system (replaced by GST in many countries)Selling price
GST Calculation:
If GST rate is \(r%\), then:
• GST Amount = \(r/100 × Price\)
• Total Price = Price + GST Amount = Price × \((1 + r/100)\)
What is Financial Literacy?
Financial literacy is understanding how money works: earning, saving, spending, budgeting, and investing.
Important Financial Concepts:
ConceptExplanationExample
BudgetingPlanning income and expensesMonthly spending plan
SavingSetting aside money for futurePutting ₹500/month in piggy bank
InvestingUsing…
Worked example
Problem: The price of a mobile phone is ₹15,000. GST is charged at 18%. Find the GST amount and the total bill amount.
- Step 1: GST amount = 18% of ₹15,000 = \(18/100 × 15000\)
- Step 2: GST = \(0.18 × 15000 = ₹2700\)
- Step 3: Total bill = Price + GST = \(15000 + 2700 = ₹17,700\)
Answer: Step 3: Total bill = Price + GST = \(15000 + 2700 = ₹17,700\)