Ratios & Proportions (Advanced) • Topic 2 of 2

Percent Problems — Discount, Tax, Markup

Percent means per hundred (out of 100). Percent problems appear in everyday life as discounts, taxes, and markups.

Problem Type	Formula
Discount	Discount = Original Price x Discount%. Sale Price = Original - Discount
Tax	Tax = Price x Tax%. Total = Price + Tax
Markup	Markup = Cost x Markup%. Selling Price = Cost + Markup
Percent Increase	(New - Old) / Old x 100%
Percent Decrease	(Old - New) / Old x 100%

Always convert percent to decimal first: 25% = 0.25

PERCENT CHANGE NUMBER LINE:

0%              100%            150%            200%
|----------------|----------------|----------------|
Original        Double           1.5x            2x

CONVERT % TO DECIMAL:
  25% = 25/100 = 0.25
  8%  = 8/100  = 0.08
  50% = 50/100 = 0.50

Solved Examples

Worked Example

A $80 shirt is 25% off. What is the sale price?

SolutionDiscount = 80 x 0.25 = $20. Sale price = 80 - 20 = $60.

Worked Example

A $50 meal has 8% tax. What is the total bill?

SolutionTax = 50 x 0.08 = $4. Total = 50 + 4 = $54.

Worked Example

A town's population grew from 2,000 to 2,500. What is the percent increase?

Solution(2500 - 2000) / 2000 x 100 = 500/2000 x 100 = 25%

Key Points

Convert % to decimal: divide by 100 (25% = 0.25)
Discount = subtract; Tax/Markup = add
Percent increase/decrease = (change / original) x 100
Original price = Sale price / (1 - discount rate)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.$10\%$ of $200$ is:

Explanation: $\tfrac{10}{100}\times200=20$.

Q2.A discount ___ the price.

Explanation: Reduces it.

Q3.Tax ___ the amount to be paid.

Explanation: Adds to it.

Q4.Sale price $=$ original price $-$

Explanation: Minus the discount.

Practice more MCQs → 📝 Assignment · 35 marks