GCSE Maths Practice: percentages

Question 7 of 10

This GCSE Maths question tests your understanding of how to calculate discounts using percentages — a skill useful in both exams and real life.

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\( \begin{array}{l}\text{A product is discounted by 15%. If the original price is }\\200,\text{ what is the discounted price?}\end{array} \)

Choose one option:

Subtract the discount rate from 100%, change it to decimal form, then multiply by the original amount. This is the most reliable way to handle any percentage reduction question.

Understanding Percentage Discounts

Percentage discounts are used in everyday life whenever a price is reduced by a certain proportion. The key idea is that a percentage tells us a part out of 100. If something is discounted by 15%, it means 15% of the original price is removed. To find the final price, we multiply the original price by the remaining percentage (100% - 15% = 85%).

Step-by-Step Method

  1. Convert the percentage discount into a decimal by dividing by 100. For example, 15% = 0.15.
  2. Subtract this from 1 to find the remaining proportion after discount: 1 - 0.15 = 0.85.
  3. Multiply the original amount by this remaining proportion: 200 × 0.85 = 170.
  4. The result, £170, is the discounted price.

Worked Examples

  • Example 1: A jacket costs £120 and is reduced by 25%. Find the new price.
    Remaining percentage = 100% - 25% = 75%.
    120 × 0.75 = £90.
  • Example 2: A laptop originally costs £800 and has a 10% discount.
    800 × 0.9 = £720.
  • Example 3: A sofa costs £600, reduced by 40%.
    600 × 0.6 = £360.

Common Mistakes

  • Adding instead of subtracting: Some students incorrectly add the discount to 100% instead of subtracting it.
  • Using the wrong decimal: Writing 0.15 as 15 or 1.15 would give the wrong answer.
  • Not multiplying the final step: Forgetting to multiply by the original value after finding the percentage left.

Real-Life Applications

This concept appears in shopping, business, and finance. Retailers use discounts to attract customers during sales seasons. Understanding percentage changes also helps compare prices, calculate savings, and budget effectively. Professionals in marketing, data analysis, and economics use similar percentage formulas to measure increases or decreases in profit, sales, or population growth.

Frequently Asked Questions

Q1: How do I calculate an increase instead of a discount?
A: Replace subtraction with addition. For a 10% increase, multiply by (1 + 0.10).

Q2: What if the discount is applied twice?

A: Apply each discount separately. For example, two 10% discounts on £100 give £100 × 0.9 × 0.9 = £81, not £80.

Q3: Can I use mental maths for this?

A: Yes. For 15% off, think of 10% (20) and 5% (10) of 200. Subtract 30 from 200 to get 170.

Study Tip

Always write down the percentage as a decimal before multiplying. This prevents confusion and ensures accuracy on GCSE Maths percentage change questions. Practice with different percentages and real-life prices until the process feels natural.

Summary

The formula for discount calculations is simple yet powerful: Final Price = Original × (1 − Discount Rate). This method is essential for both GCSE exams and real-world financial literacy.