Ravi's salary grew by 20%, so he could save 30% more. What is the percentage change in expenditure if his initial savings were 25%?

To find the percentage change in Ravi's expenditure, we need to carefully analyze the relationship between his salary, savings, and expenditure.

### Step 1: Define the initial amounts

Let's assume:
- Ravi's initial salary is \( S \).
- His initial savings are 25% of his salary, so initial savings = \( 0.25S \).
- His initial expenditure would be the remaining 75% of his salary, so initial expenditure = \( 0.75S \).

### Step 2: Calculate the new salary and new savings

Ravi's salary increases by 20%, so the new salary is:
\[
\text{New Salary} = S + 0.2S = 1.2S
\]

Ravi's savings increase by 30%, so the new savings are:
\[
\text{New Savings} = 1.3 \times \text{Initial Savings} = 1.3 \times 0.25S = 0.325S
\]

### Step 3: Calculate the new expenditure

The new expenditure is the difference between the new salary and the new savings:
\[
\text{New Expenditure} = \text{New Salary} - \text{New Savings} = 1.2S - 0.325S = 0.875S
\]

### Step 4: Calculate the percentage change in expenditure

To find the percentage change in expenditure, we compare the new expenditure to the initial expenditure:

\[
\text{Percentage change in expenditure} = \frac{\text{New Expenditure} - \text{Initial Expenditure}}{\text{Initial Expenditure}} \times 100\%
\]

Substitute the values:
\[
\text{Percentage change in expenditure} = \frac{0.875S - 0.75S}{0.75S} \times 100\% = \frac{0.125S}{0.75S} \times 100\% = \frac{0.125}{0.75} \times 100\% = \frac{1}{6} \times 100\% \approx 16.67\%
\]

### Final Answer:
The percentage change in Ravi's expenditure is approximately **16.67%**.

Do you need any further clarification or details?

---

1. What if Ravi's salary increased by 15% instead?
2. How would the expenditure change if his savings initially were 20%?
3. What is the percentage change in savings?
4. What if his new savings were 40% more instead of 30%?
5. How does the expenditure change if the salary does not increase?
6. What would happen if Ravi's salary decreased by 10%?
7. How can you calculate the change if savings percentage changes first?
8. Can this method be applied to other types of expenses?

**Tip:** When calculating percentage changes, always express the change relative to the original amount to avoid confusion.

Explore how to calculate the percentage change in expenditure when Ravi's salary increases by 20% and his initial savings are 25%. Understand the mathematical relationship between salary, savings, and expenditure. Suitable for Grades 9-12.

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