Comparing Quantities

• Ratios and Percentages

  • Ratio: Comparing two quantities with same units
  • Percentage: Expressing a quantity out of 100
  • Conversion Methods
    • Ratio to Percentage: Multiply by 100
    • Percentage to Fraction: Divide by 100
  • Percentage Change
    • Increase % = (Increase Amount / Original Value) × 100
    • Decrease % = (Decrease Amount / Original Value) × 100

• Discount

  • Reduction on Marked Price (MP)
  • Discount Amount = MP - SP
  • Discount % = (Discount / MP) × 100
  • Selling Price (SP) = MP - Discount

• Profit and Loss

  • Cost Price (CP): Buying price + overhead charges
  • Selling Price (SP): Price at which an item is sold
  • Profit (Gain)
    • Condition: SP > CP
    • Profit = SP - CP
    • Profit % = (Profit / CP) × 100
  • Loss
    • Condition: CP > SP
    • Loss = CP - SP
    • Loss % = (Loss / CP) × 100

• Sales Tax / VAT / GST

  • Tax charged by government on sale of goods
  • Added directly to the bill amount
  • Tax Amount = Tax Rate % of Cost Price
  • Final Bill Amount = Cost Price + Tax

• Simple Interest (SI)

  • Interest calculated uniformly on original principal
  • Formula: SI = (P × R × T) / 100
    • P: Principal
    • R: Rate of Interest per annum
    • T: Time period in years
  • Total Amount (A) = P + SI

• Compound Interest (CI)

  • Interest calculated on principal + previously earned interest
  • Formula for Amount (A)
    • Compounded Annually: A = P(1 + R/100)^n
    • Compounded Half-Yearly: Rate = R/2, Time = 2n
  • CI Formula: CI = A - P
  • Key Difference: CI > SI for time period > 1 year

• Applications of Compound Interest

  • Growth Calculation: Population increase → A = P(1 + R/100)^n
  • Depreciation: Reduction in value of items over time → A = P(1 - R/100)^n