Topics › KS3 › Ratio & proportion
Percentage change
-
The price of a ticket rises from £40 to £50. What is the percentage increase?
A
Option A:
$20\%$
B
Option B:
$10\%$
C
Option C:
$125\%$
D
Option D:
$25\%$
Answer and misconceptions
A
Option A:
$20\%$
✗
Divides the change by the new amountWorks out $\frac{10}{50}$; percentage change compares the change with the original amount, $\frac{10}{40}$.
B
Option B:
$10\%$
✗
Gives the actual change as the percentageThe price went up by £10, but £10 is not $10\%$ of £40.
C
Option C:
$125\%$
✗
Gives the new amount as a percentage of the originalWorks out $\frac{50}{40} = 125\%$; the increase is $125\% - 100\% = 25\%$.
D
Option D:
$25\%$
✓ Correct
-
After a $20\%$ increase, a coat costs £60. What was the price before the increase?
A
Option A:
£48
B
Option B:
£72
C
Option C:
£50
D
Option D:
£40
Answer and misconceptions
A
Option A:
£48
✗
Takes $20\%$ of the new price offWorks out £60 − $20\%$ of £60. The $20\%$ was of the original price, so £60 is $120\%$: £60 ÷ 1.2.
B
Option B:
£72
✗
Applies the increase again instead of undoing itWorks out £60 × 1.2; to go back to the original, divide by 1.2.
C
Option C:
£50
✓ Correct
D
Option D:
£40
✗
Treats $20\%$ as £20Subtracts £20 from £60; a percentage is a fraction of an amount, not a number of pounds.
-
£200 is invested at $5\%$ compound interest per year. How much is it worth after 2 years?
A
Option A:
£220.50
B
Option B:
£220
C
Option C:
£20.50
D
Option D:
£210
Answer and misconceptions
A
Option A:
£220.50
✓ Correct
B
Option B:
£220
✗
Uses simple interest instead of compoundAdds £10 each year; with compound interest the second year earns $5\%$ of £210, which is £10.50.
C
Option C:
£20.50
✗
Gives only the interestWorks out the interest, £20.50, but not the total value: £200 + £20.50.
D
Option D:
£210
✗
Works out only one yearStops after the first year; the question asks for 2 years.
-
Which calculation increases £80 by $3.5\%$?
A
Option A:
£80 × 1.35
B
Option B:
£80 × 1.035
C
Option C:
£80 × 0.035
D
Option D:
£80 × 3.5
Answer and misconceptions
A
Option A:
£80 × 1.35
✗
Writes $3.5\%$ as $0.35$$3.5\% = 3.5 \div 100 = 0.035$, so the multiplier is $1 + 0.035 = 1.035$.
B
Option B:
£80 × 1.035
✓ Correct
C
Option C:
£80 × 0.035
✗
Uses the multiplier for the increase only£80 × 0.035 gives the increase (£2.80), not the new amount.
D
Option D:
£80 × 3.5
✗
Uses the percentage as the multiplierMultiplies by 3.5, which makes the amount 3.5 times bigger.
-
A car loses $10\%$ of its value each year. What is the total percentage decrease after 2 years?
A
Option A:
$20\%$
B
Option B:
$81\%$
C
Option C:
$19\%$
D
Option D:
$1\%$
Answer and misconceptions
A
Option A:
$20\%$
✗
Adds the percentage changesThe second $10\%$ is taken from a smaller value, so the total drop is less than $20\%$: $0.9 \times 0.9 = 0.81$.
B
Option B:
$81\%$
✗
Gives the remaining value as the decreaseThe car is worth $81\%$ of its value after 2 years, so it has lost $100\% - 81\% = 19\%$.
C
Option C:
$19\%$
✓ Correct
D
Option D:
$1\%$
✗
Multiplies the percentagesWorks out $10\% \times 10\% = 1\%$; the multipliers $0.9 \times 0.9$ should be used instead.