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AQA GCSE · Question 10 · Number
384 000 electric cars were sold this year.
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This is 20% more than last year.
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How many were sold last year?
384 000 electric cars were sold this year.
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This is 20% more than last year.
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How many were sold last year?
How to approach this question
1. Identify that this is a reverse percentage problem. You are given the final amount after a percentage increase and need to find the original amount.
2. Determine the multiplier for a 20% increase. A 20% increase means you have 100% + 20% = 120% of the original amount.
3. Convert this percentage to a decimal multiplier (120 / 100 = 1.2).
4. Set up an equation: Original Amount × 1.2 = 384 000.
5. Solve for the Original Amount by dividing 384 000 by the multiplier.
Full Answer
This problem requires us to find the original value before a percentage increase. This is known as a reverse percentage calculation.
The number of cars sold this year (384,000) is 20% *more* than last year.
This means that 384,000 represents 100% (last year's amount) + 20% (the increase).
So, 384,000 = 120% of last year's sales.
To find 100%, we can first find 1% and then multiply by 100, or use a decimal multiplier.
Using the multiplier method is faster:
120% as a decimal is 1.2.
Let L be the number of cars sold last year.
L × 1.2 = 384,000
L = 384,000 ÷ 1.2
L = 320,000
So, 320,000 cars were sold last year.
Common mistakes
✗ The most common mistake is to calculate 20% of 384,000 and subtract it. This would be finding 80% of the current year's sales, not reversing a 20% increase from the previous year. (384,000 × 0.8 = 307,200, which is incorrect).
✗ Dividing by 0.20 instead of 1.20.
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