Percentage Increase and Decrease

Use the percentage increase formula: New Value = Original Value $\times$ (1 + Percentage Change).

As a decimal, $10\%$ is $10÷100=0.1$, so the multiplier is $1+0.1=1.1$.

New price: $50\times 1.1=55$, so the book now costs £55.

You can check it: $10\%$ of £50 is £5, and £50 + £$5=$ £55.

Use the percentage decrease formula: New Value = Original Value $\times$ (1 − Percentage Change).

As a decimal, $30\%$ is $30÷100=0.3$, so the multiplier is $1-0.3=0.7$.

Sale price: $200\times 0.7=140$, so the table costs £140.

You can check it: $30\%$ of £200 is £60, and £200 − £$60=$ £140.

Use the percentage decrease formula: New Value = Original Value $\times$ (1 − Percentage Change).

As a decimal, $15\%$ is $15÷100=0.15$, so the multiplier is $1-0.15=0.85$.

Price paid: $20\times 0.85=17$, so you pay £17.

Or work out the discount first: $15\%$ of £20 is £3, and £20 − £$3=$ £17. Take care with $1-0.15$: it is 0.85, not 0.95.

This is a reverse percentage: the £60 is the price after the discount, not the original.

Start with New Value = Original Value $\times$ (1 − Percentage Change). The multiplier is $1-0.25=0.75$, so $60=\text{Original}\times 0.75$.

To undo the multiplication, divide: $60÷0.75=80$, so the original price was £80.

Check: $25\%$ of £80 is £20, and £80 − £$20=$ £60.

Use the percentage increase formula: New Value = Original Value $\times$ (1 + Percentage Change).

As a decimal, $12\%$ is $12÷100=0.12$, so the multiplier is $1+0.12=1.12$ (not 1.2, which would be a $20\%$ increase).

New price: $600\times 1.12=672$, so the laptop now costs £672.

Check: $12\%$ of £600 is £72, and £600 + £$72=$ £672.

Apply the two discounts one after the other, not added together.

First the $30\%$ off: $100\times (1-0.30)=100\times 0.7=70$, so the price drops to £70.

Then the $10\%$ off that reduced price: $70\times (1-0.10)=70\times 0.9=63$.

So you pay £63. Taking $40\%$ off in one go would give £60, which is wrong: the second discount applies to £70, not to the original £100.