Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
56%
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%.
| Particulars | Initial (₹) | Change | New (₹) |
|---|---|---|---|
| Income | 100 | +29% | 129 |
| Savings | 25 | 39 | |
| Expenditure | 75 | +20% | 90 |
Summary of Steps
- Assume an initial income (e.g., 100).
- Calculate initial savings (25% of income) and initial expenditure (Income - Savings).
- Calculate the new income after the 29% increase.
- Calculate the new expenditure after the 20% increase.
- Calculate the new savings (New Income - New Expenditure).
- Calculate the absolute increase in savings (New Savings - Initial Savings).
- Calculate the percentage increase in savings using the formula: \( \frac{\text{Increase}}{\text{Original}} \times 100\% \).
Revision Table: Income, Expenditure, and Savings Concepts
| Term | Definition | Relationship |
|---|---|---|
| Income | Money received, usually periodically, in return for work or through investments. | Income = Expenditure + Savings |
| Expenditure | Money spent on goods and services. | |
| Savings | The part of income that is not spent. |
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).
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