Rama's expenditures and savings are in the ratio 5:3. If her income increases by 12% and expenditure by 15%, then by how much per cent do her savings Increase ?

Options

A. 12
B. 7
C. 8
D. 13

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Define Variables
Let Rama's expenditures be represented as \( 5x \) and her savings as \( 3x \), based on the given ratio of expenditures to savings (5:3).

### Step 2: Calculate Income
Rama's income can be calculated by adding her expenditures and savings:
\[ \text{Income} = \text{Expenditures} + \text{Savings} = 5x + 3x = 8x \]

### Step 3: Calculate New Income After Increase
Rama's income increases by 12%. Therefore, her new income will be:
\[ \text{New Income} = \text{Old Income} + 12\% \text{ of Old Income} = 8x + 0.12 \times 8x = 8x \times \left(1 + \frac{12}{100}\right) = 8x \times 1.12 = 8.96x \]

### Step 4: Calculate New Expenditure After Increase
Rama's expenditures increase by 15%. Therefore, her new expenditures will be:
\[ \text{New Expenditures} = \text{Old Expenditures} + 15\% \text{ of Old Expenditures} = 5x + 0.15 \times 5x = 5x \times \left(1 + \frac{15}{100}\right) = 5x \times 1.15 = 5.75x \]

### Step 5: Calculate New Savings
Now, we can calculate her new savings after the increases:
\[ \text{New Savings} = \text{New Income} - \text{New Expenditures} = 8.96x - 5.75x = 3.21x \]

### Step 6: Calculate Increase in Savings
To find the increase in savings, we subtract the old savings from the new savings:
\[ \text{Increase in Savings} = \text{New Savings} - \text{Old Savings} = 3.21x - 3x = 0.21x \]

### Step 7: Calculate Percentage Increase in Savings
Finally, to find the percentage increase in savings, we use the formula:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase in Savings}}{\text{Old Savings}}\right) \times 100 = \left(\frac{0.21x}{3x}\right) \times 100 \]
\[ = \left(\frac{0.21}{3}\right) \times 100 = 7\% \]

### Conclusion
Thus, the percentage increase in Rama's savings is **7%**.

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