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Lesson 10

Advanced Problems

Challenge yourself with complex percentage scenarios.

  • advanced

📚 Advanced Percentage Problems

Now let's tackle some challenging problems that combine multiple concepts!

🧮 Complex Problem

A store marks up items by 60%, then offers a "40% off" sale. Is the store making or losing money?

1
Cost to store: $100
2
After 60% markup: $100 × 1.60 = $160
3
After 40% discount: $160 × 0.60 = $96

The store loses $4 per item!

Frequently Asked Questions

How do I solve a problem with several percentage steps?

Take one step at a time and carry the result forward: apply the discount, then the tax, then the tip, each to the number the previous step produced.

What is the most common mistake in percentage problems?

Using the wrong base. A percentage is always of something; check whether it is of the original, the new value or the total before you multiply.

Practice

Work each one out, then check yourself.

  1. Company A's profits increased by 25% in Year 1 and decreased by 20% in Year 2. If they started with $1,000,000, what's the final profit?

    Hint: Year 1: $1M × 1.25 = $1.25M. Year 2: $1.25M × 0.80 = ?

    Show answer

    1000000

Final Quiz

0/3

Test what you learned. Pick the correct answer for each question.

  1. A stock rose 25% then fell 20%. Net change?

    A stock rose 25% then fell 20%. Net change?

  2. You need $500 final. The price has 10% off and 8% tax. Approximate pre-discount price?

    You need $500 final. The price has 10% off and 8% tax. Approximate pre-discount price?

  3. Going from 40% to 60% market share is what relative increase?

    Going from 40% to 60% market share is what relative increase?