Renu saves 30% of her income. If her savings increases by 30% and the expenditure increases by 25%, then the percentage increase in her income is:

Options

A. 30
B. `25.8`
C. `26.5`
D. `15`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define Variables
Let Renu's total income be \( I \). According to the problem, Renu saves 30% of her income. Therefore, her savings \( S \) can be expressed as:
\[ S = 0.30 \times I \]
This means her savings are \( \frac{3}{10} \) of her income.

### Step 2: Calculate Expenditure
Since savings and expenditure together make up the total income, we can express her expenditure \( E \) as:
\[ E = I - S = I - 0.30I = 0.70I \]
Thus, her expenditure is \( \frac{7}{10} \) of her income.

### Step 3: Determine New Savings and Expenditure
According to the problem, Renu's savings increase by 30%. Therefore, her new savings \( S' \) will be:
\[ S' = S + 0.30S = 1.30S = 1.30 \times 0.30I = 0.39I \]

Similarly, her expenditure increases by 25%. Therefore, her new expenditure \( E' \) will be:
\[ E' = E + 0.25E = 1.25E = 1.25 \times 0.70I = 0.875I \]

### Step 4: Calculate New Income
Now, the new total income \( I' \) can be expressed as the sum of her new savings and new expenditure:
\[ I' = S' + E' = 0.39I + 0.875I = 1.265I \]

### Step 5: Calculate Percentage Increase in Income
The percentage increase in income can be calculated using the formula:
\[ \text{Percentage Increase} = \left( \frac{I' - I}{I} \right) \times 100 \]
Substituting \( I' \):
\[ \text{Percentage Increase} = \left( \frac{1.265I - I}{I} \right) \times 100 = \left( \frac{0.265I}{I} \right) \times 100 = 26.5\% \]

### Conclusion
Thus, the percentage increase in Renu's income is \( \boxed{26.5\%} \).

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