To calculate the percentage increase, use the formula:

$\text{Percentage Increase} = \left( \frac{\text{New Number} - \text{Original Number}}{\text{Original Number}} \right) \times 100$

Let's calculate the percentage increase for each case:

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a. $50 \to 60$: $\text{Percentage Increase} = \left( \frac{60 - 50}{50} \right) \times 100 = \left( \frac{10}{50} \right) \times 100 = 20\%$

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b. $75 \to 135$: $\text{Percentage Increase} = \left( \frac{135 - 75}{75} \right) \times 100 = \left( \frac{60}{75} \right) \times 100 = 80\%$

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c. $40 \to 84$: $\text{Percentage Increase} = \left( \frac{84 - 40}{40} \right) \times 100 = \left( \frac{44}{40} \right) \times 100 = 110\%$

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d. $30 \to 31.5$: $\text{Percentage Increase} = \left( \frac{31.5 - 30}{30} \right) \times 100 = \left( \frac{1.5}{30} \right) \times 100 = 5\%$

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e. $18 \to 33.3$: $\text{Percentage Increase} = \left( \frac{33.3 - 18}{18} \right) \times 100 = \left( \frac{15.3}{18} \right) \times 100 \approx 85\%$

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f. $4 \to 13$: $\text{Percentage Increase} = \left( \frac{13 - 4}{4} \right) \times 100 = \left( \frac{9}{4} \right) \times 100 = 225\%$

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Final Answers:

• a. 20%
• b. 80%
• c. 110%
• d. 5%
• e. 85%
• f. 225%

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Do you want further explanations or have any questions?
Here are 5 related questions to deepen your understanding:

1. How do you calculate a percentage decrease instead of an increase?
2. What is the percentage increase from $100 \to 120$?
3. If a price increases by 15%, what is the multiplier to find the new price?
4. Can you explain why percentage increase is relative to the original number?
5. How would you apply percentage increase in real-world contexts, such as discounts or profits?

Tip: Always check if the percentage increase is based on the original value or another reference for accurate results!