Anita spends `68%` of her monthly income .If her monthly income increases by `40%` and the expenditure increases by `30%` ,then by what percent does her saving increase ?

Options

A. `61.25%`
B. `54.25%`
C. `48.50%`
D. `62.50%`

Answer

To solve the problem step by step, let's denote Anita's monthly income and expenditure clearly.

### Step 1: Assume Monthly Income
Let Anita's monthly income be \( I = 100 \) (this is a convenient assumption to simplify calculations).

### Step 2: Calculate Monthly Expenditure
Anita spends \( 68\% \) of her income. Therefore, her expenditure \( E \) is:
\[ E = 68\% \text{ of } I = \frac{68}{100} \times 100 = 68 \]

### Step 3: Calculate Monthly Savings
Her savings \( S \) can be calculated as:
\[ S = I - E = 100 - 68 = 32 \]

### Step 4: Calculate New Monthly Income
If her income increases by \( 40\% \), her new income \( I' \) will be:
\[ I' = I + 40\% \text{ of } I = 100 + \frac{40}{100} \times 100 = 100 + 40 = 140 \]

### Step 5: Calculate New Monthly Expenditure
If her expenditure increases by \( 30\% \), her new expenditure \( E' \) will be:
\[ E' = E + 30\% \text{ of } E = 68 + \frac{30}{100} \times 68 = 68 + 20.4 = 88.4 \]

### Step 6: Calculate New Monthly Savings
Now, we can calculate her new savings \( S' \):
\[ S' = I' - E' = 140 - 88.4 = 51.6 \]

### Step 7: Calculate Increase in Savings
The increase in savings can be calculated as:
\[ \text{Increase in Savings} = S' - S = 51.6 - 32 = 19.6 \]

### Step 8: Calculate Percentage Increase in Savings
Finally, the percentage increase in savings is given by:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Savings}}{S} \right) \times 100 = \left( \frac{19.6}{32} \right) \times 100 \approx 61.25\% \]

### Final Answer
Thus, the percentage increase in Anita's savings is approximately \( 61.25\% \).

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