Percentage Increase and Decrease

🔮 Formula for Percentage Increase and Decrease

$$
\large \text{Original value} \times \left( 1 \pm \text{Percentage Change} \right) = \text{New value}
$$

• Use + for an increase
• Use − for a decrease

For example: 

• Increase: £100 increases by 20% → 100 × (1 + 0.20) = £120
• Decrease: £100 decreases by 10% → 100 × (1 − 0.10) = £90

🌟 Example 1: Percentage Increase

Q: Last month, your maths score was 60. This month, it goes up by 20%.
What is your new score?

$$ 60 \times (1 + 20\%) = 60 \times (1 + 0.2) = 60 \times 1.2 = 72$$

Answer: So your new score is 72. Great improvement! 🥳

🌟 Example 2: Percentage Decrease

Q: A jacket was originally $90, but now there’s a 30% discount.
How much do you pay?

$$ 90 \times (1 – 30\%) = 90 \times (1 – 0.3) = 90 \times 0.7 = 63$$

So now you only need to pay \$63. What a bargain! 🥳

🔮 What is Reverse Percentage?

Sometimes you know the final amount after a percentage increase or decrease (such as a discount or a price rise), but you need to work out the original amount before the change. This is called a reverse percentage.

🌟 Example of Solving Reverse Percentage Problem

You paid $36 for a concert ticket after a 40% student discount.
What was the original price?

1. Set up the equation:
   original price × (1 − 40%) = 36

2. Convert the percentage to a decimal:
   original price × 0.6 = 36

3. Solve for the original price:
   original price = 36 ÷ 0.6

4. Final answer:
   original price = $60

So, the original price of the concert ticket is $60.