A girl spends 76% of her income. If her income increases by 18% and her expenditure increases by 25% then what is the percentage increase or decrease in her savings(correct to one decimal place)?

Options

A. 6.9% decrease
B. 4.2%decrease
C. 5.7% increase
D. 8.4% increase

Answer

To solve the problem step by step, we will first determine the girl's initial income, expenditure, and savings. Then we will calculate the new income and expenditure after the increases, and finally, we will find the percentage change in her savings.

### Step 1: Determine Initial Income and Expenditure
Let the girl's initial income be \( I = 100 \) (for simplicity).

Since she spends 76% of her income:
\[ \text{Expenditure} = 76\% \text{ of } I = 0.76 \times 100 = 76 \]

### Step 2: Calculate Initial Savings
Savings can be calculated as:
\[ \text{Savings} = \text{Income} - \text{Expenditure} = 100 - 76 = 24 \]

### Step 3: Calculate New Income
The income increases by 18%, so the new income is:
\[ \text{New Income} = I + (18\% \text{ of } I) = 100 + (0.18 \times 100) = 100 + 18 = 118 \]

### Step 4: Calculate New Expenditure
The expenditure increases by 25%, so the new expenditure is:
\[ \text{New Expenditure} = \text{Expenditure} + (25\% \text{ of Expenditure}) = 76 + (0.25 \times 76) = 76 + 19 = 95 \]

### Step 5: Calculate New Savings
New savings can be calculated as:
\[ \text{New Savings} = \text{New Income} - \text{New Expenditure} = 118 - 95 = 23 \]

### Step 6: Calculate the Change in Savings
Now we find the change in savings:
\[ \text{Change in Savings} = \text{New Savings} - \text{Initial Savings} = 23 - 24 = -1 \]

### Step 7: Calculate the Percentage Change in Savings
To find the percentage change in savings:
\[ \text{Percentage Change} = \left( \frac{\text{Change in Savings}}{\text{Initial Savings}} \right) \times 100 = \left( \frac{-1}{24} \right) \times 100 \approx -4.1667 \]

Rounding to one decimal place, the percentage change in savings is:
\[ \text{Percentage Change} \approx -4.2\% \]

### Final Answer
The percentage decrease in her savings is **4.2%**.