Here is a sign in a shop.
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Is the sign correct? Give a reason for your answer.
How to approach this question
1. Consider the effect of successive percentage changes. They are not simply added together.
2. Use a multiplier method. A 20% discount is equivalent to multiplying by (1 - 0.20) = 0.8. A 10% discount is equivalent to multiplying by (1 - 0.10) = 0.9.
3. Apply the multipliers sequentially to an initial value (e.g., £100 or a variable P).
4. Calculate the overall multiplier by multiplying the individual multipliers (0.8 × 0.9).
5. Convert the overall multiplier back into a percentage saving and compare it to 30%.
Full Answer
The sign is incorrect because percentage discounts cannot be simply added together when they are applied sequentially. The second discount is calculated on the already reduced price, not the original price.
Let's test this with an example price of £100.
1. **First discount (20%):**
20% of £100 is £20.
The reduced price is £100 - £20 = £80.
2. **Second discount (10%):**
This 10% is taken off the *reduced price* of £80.
10% of £80 is £8.
The final price is £80 - £8 = £72.
3. **Total Saving:**
The total amount saved is £100 - £72 = £28.
A saving of £28 on an original price of £100 is a 28% saving.
Alternatively, using multipliers:
- A 20% discount means you pay 80% (multiplier of 0.8).
- A 10% discount means you pay 90% (multiplier of 0.9).
- The combined effect is 0.8 × 0.9 = 0.72.
- Paying 72% of the original price means a saving of 100% - 72% = 28%.
Since 28% is not equal to 30%, the sign is incorrect.
Common mistakes
✗ Simply adding the percentages (20% + 10% = 30%) and concluding the sign is correct.
✗ Providing an incomplete explanation, e.g., just saying "No, it's wrong" without showing why.
Expert