A person saves `6%` of income. After 2 years his income is increased by `15%` but his savings remain the same. Find the percentage increase in his expenditure

Answer

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

### Step 1: Determine Current Income and Savings
Let the current income of the person be \(100\) rupees. Since the person saves \(6\%\) of their income, we can calculate the savings.

**Calculation:**
\[ \text{Savings} = 6\% \text{ of } 100 = \frac{6}{100} \times 100 = 6 \text{ rupees} \]

### Step 2: Calculate Current Expenditure
To find the current expenditure, we subtract the savings from the income.

**Calculation:**
\[ \text{Expenditure} = \text{Income} - \text{Savings} = 100 - 6 = 94 \text{ rupees} \]

### Step 3: Determine New Income After 2 Years
After 2 years, the income increases by \(15\%\). We calculate the new income.

**Calculation:**
\[ \text{New Income} = \text{Current Income} + 15\% \text{ of Current Income} = 100 + \frac{15}{100} \times 100 = 100 + 15 = 115 \text{ rupees} \]

### Step 4: Determine New Savings
The problem states that the savings remain the same, which means the savings after 2 years is still \(6\) rupees.

### Step 5: Calculate New Expenditure
Now, we calculate the new expenditure using the new income and the unchanged savings.

**Calculation:**
\[ \text{New Expenditure} = \text{New Income} - \text{Savings} = 115 - 6 = 109 \text{ rupees} \]

### Step 6: Calculate Increase in Expenditure
Next, we find the increase in expenditure by subtracting the old expenditure from the new expenditure.

**Calculation:**
\[ \text{Increase in Expenditure} = \text{New Expenditure} - \text{Old Expenditure} = 109 - 94 = 15 \text{ rupees} \]

### Step 7: Calculate Percentage Increase in Expenditure
Finally, we calculate the percentage increase in expenditure using the formula:

\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Expenditure}}{\text{Old Expenditure}} \right) \times 100 \]

**Calculation:**
\[ \text{Percentage Increase} = \left( \frac{15}{94} \right) \times 100 \approx 15.95\% \]

### Final Answer
The percentage increase in his expenditure is approximately \(15.95\%\).

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