GCSE Maths Practice: percentages

Question 8 of 10

This GCSE Maths question tests your ability to calculate the final price after applying a percentage discount — a key skill for both exams and everyday shopping.

‹ ›

\( \begin{array}{l}\text{A store offers 15% discount. The original price is 200.}\\\text{What is the price after discount?}\end{array} \)

Choose one option:

Subtract the discount rate from 100% to find what remains, then convert to a decimal before multiplying. This is the safest and quickest way to calculate discounts in GCSE problems.

Understanding Percentage Discounts

Percentage discounts are a common feature in both GCSE Maths and real life. They are used whenever a price is reduced by a certain proportion. A discount shows how much of the original cost is taken off, and the new price represents what remains. Learning to calculate this accurately helps you handle money problems, business questions, and exam problems involving percentage change.

The key formula is:
Discounted Price = Original × (1 − Discount Rate).

Step-by-Step Method

  1. Write down the percentage discount and convert it into a decimal by dividing by 100. For example, 20% becomes 0.20.
  2. Subtract this value from 1: 1 − 0.20 = 0.80.
  3. Multiply the original amount by this new decimal. The result gives the price after discount.

Worked Examples (Different Values)

  • Example 1: A pair of shoes costs £100 and is reduced by 10%.
    Multiplier = 0.90 → 100 × 0.90 = £90.
  • Example 2: A computer monitor costs £320 with a 25% discount.
    Multiplier = 0.75 → 320 × 0.75 = £240.
  • Example 3: A sofa originally costs £500 and is reduced by 30%.
    Multiplier = 0.70 → 500 × 0.70 = £350.

Common Mistakes

  • Adding instead of subtracting: A frequent mistake is to add the percentage rather than subtract it, which gives a higher total instead of a discount.
  • Incorrect decimal conversion: Writing 0.5 instead of 0.05 for 5% drastically changes the result.
  • Forgetting the multiplier step: Some students calculate the discount amount but forget to subtract it from the original price.

Real-Life Applications

Discounts are everywhere — from sales events and coupons to business promotions. In finance, they also appear when calculating reductions in value, such as depreciation. Knowing how to calculate the final price after a percentage discount helps in budgeting, comparing deals, and understanding savings.

For instance, if a laptop is advertised with “20% off,” you can quickly estimate whether the saving is worth it. This same calculation appears in GCSE Maths papers in the context of price reductions, population decreases, and data comparisons.

Frequently Asked Questions

Q1: How is a 15% discount different from taking off £15?

A: A 15% discount depends on the original value — it’s not a fixed £15 unless the item costs £100. Always calculate the actual percentage of the original amount.

Q2: Can discounts be combined?

A: Yes, but apply them one after the other. For example, two 10% discounts on £100: 100 × 0.9 × 0.9 = £81, not £80.

Q3: What is the fastest mental method?

A: Find 10% of the price and then half it for 5%, if needed. Subtract the total discount from the original value.

GCSE Study Tip

Always use the multiplier form (1 − rate) for discounts. This single step avoids errors with subtraction and helps in multi-step word problems involving increases and decreases together.

Summary

Percentage discounts form a core part of GCSE Maths and real-life financial reasoning. The formula Final Price = Original × (1 − Discount Rate) allows you to find sale prices, budget reductions, and value decreases quickly. Practising with different examples ensures confidence in both exams and daily money management.