Calculating Percentage Increase in Radha's Savings

This problem involves understanding the relationship between income, expenditure, and savings and how changes in income and expenditure affect savings. The fundamental equation is:

Income = Expenditure + Savings

Initial Situation Analysis

We are given that Radha saves 25% of her income. Let's assume an initial income to make calculations easier. A common approach is to assume the initial income is ₹100.

• Assume Initial Income = ₹100
• Initial Savings = 25% of Initial Income
• Initial Savings = \( \frac{25}{100} \times 100 \) = ₹25
• Initial Expenditure = Initial Income - Initial Savings
• Initial Expenditure = ₹100 - ₹25 = ₹75

So, initially, if income is ₹100, savings are ₹25, and expenditure is ₹75.

Changes in Income and Expenditure

Now, let's calculate the new income and new expenditure based on the given percentage increases.

• Income increases by 29%.
• New Income = Initial Income + 29% of Initial Income
• New Income = \( 100 + \frac{29}{100} \times 100 \) = \( 100 + 29 \) = ₹129

The new income is ₹129.

• Expenditure increases by 20%.
• New Expenditure = Initial Expenditure + 20% of Initial Expenditure
• New Expenditure = \( 75 + \frac{20}{100} \times 75 \)
• New Expenditure = \( 75 + \frac{1}{5} \times 75 \)
• New Expenditure = \( 75 + 15 \) = ₹90

The new expenditure is ₹90.

Calculating New Savings

Using the fundamental equation (Income = Expenditure + Savings), we can find the new savings:

• New Savings = New Income - New Expenditure
• New Savings = ₹129 - ₹90
• New Savings = ₹39

The new savings are ₹39.

Calculating Percentage Increase in Savings

The initial savings were ₹25, and the new savings are ₹39. The increase in savings is:

• Increase in Savings = New Savings - Initial Savings
• Increase in Savings = ₹39 - ₹25 = ₹14

To find the percentage increase in savings, we compare the increase in savings to the initial savings:

• Percentage Increase in Savings = \( \frac{\text{Increase in Savings}}{\text{Initial Savings}} \times 100\% \)
• Percentage Increase in Savings = \( \frac{14}{25} \times 100\% \)
• Percentage Increase in Savings = \( 14 \times \frac{100}{25} \% \)
• Percentage Increase in Savings = \( 14 \times 4 \% \)
• Percentage Increase in Savings = 56%

Thus, Radha's savings increase by 56%.

Summary of Steps

1. Assume an initial income (e.g., 100).
2. Calculate initial savings (25% of income) and initial expenditure (Income - Savings).
3. Calculate the new income after the 29% increase.
4. Calculate the new expenditure after the 20% increase.
5. Calculate the new savings (New Income - New Expenditure).
6. Calculate the absolute increase in savings (New Savings - Initial Savings).
7. Calculate the percentage increase in savings using the formula: \( \frac{\text{Increase}}{\text{Original}} \times 100\% \).

Revision Table: Income, Expenditure, and Savings Concepts

Additional Information: Percentage Change

Percentage change is a way to express the change in a value as a percentage of the original value. The formula is:

Percentage Change = \( \frac{\text{Change in Value}}{\text{Original Value}} \times 100\% \)

If the change is an increase, it's a percentage increase. If it's a decrease, it's a percentage decrease.

In this problem, we calculated the percentage increase in Radha's savings by comparing the increase in savings (₹14) to the initial savings (₹25).