AQA GCSE · Question 24 · Ratio Proportion and Rates of Change
384 000 electric cars were sold this year. This is 20% more than last year. How many were sold last year?
How to approach this question
1. "20% more than last year" means this year's sales are 100% + 20% = 120% of last year's sales.
2. Convert this percentage to a decimal multiplier: 120% = 1.20.
3. Let L be the number of cars sold last year. The equation is L * 1.20 = 384 000.
4. To find L, we need to do the reverse operation. Divide this year's sales by the multiplier.
5. L = 384 000 / 1.20.
6. Calculate the result: L = 320 000.
Full Answer
320 000
This is a reverse percentage problem.
This year's sales are "20% more than last year". This means this year's sales are 100% (last year's amount) + 20% (the increase) = 120% of last year's sales.
So, we can say:
120% of last year's sales = 384 000
To work with this, we convert the percentage to a decimal multiplier:
120% = 120 / 100 = 1.2
Let L be the number of cars sold last year. The equation is:
L × 1.2 = 384 000
To find L, we need to divide 384 000 by 1.2:
L = 384 000 / 1.2
L = 320 000
So, 320 000 electric cars were sold last year.
Common mistakes
✗ The most common mistake is to calculate 20% of 384 000 and subtract it. This is incorrect because the 20% increase was based on last year's smaller number, not this year's larger number. (384000 * 0.8 = 307200 is the wrong answer).
✗ Dividing by 1.2 incorrectly.
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