Ratio of Rama's expenditure and saving is 5 : 3. If his income is increased by `12%` and expenditure is increased by `15%` , find his savings increase

Answer

To solve the problem step by step, let's denote Rama's expenditure and savings based on the given ratio.

### Step 1: Define Variables
Let Rama's expenditure be \( 5x \) and his savings be \( 3x \), where \( x \) is a common multiplier.

### Step 2: Calculate Total Income
Rama's total income can be calculated as:
\[ \text{Income} = \text{Expenditure} + \text{Savings} = 5x + 3x = 8x \]

### Step 3: Calculate New Income
If Rama's income is increased by \( 12\% \), the new income becomes:
\[ \text{New Income} = \text{Old Income} + 12\% \text{ of Old Income} = 8x + 0.12 \times 8x = 8x(1 + 0.12) = 8x \times 1.12 = 8.96x \]

### Step 4: Calculate New Expenditure
If Rama's expenditure is increased by \( 15\% \), the new expenditure becomes:
\[ \text{New Expenditure} = \text{Old Expenditure} + 15\% \text{ of Old Expenditure} = 5x + 0.15 \times 5x = 5x(1 + 0.15) = 5x \times 1.15 = 5.75x \]

### Step 5: Calculate New Savings
Now, we can calculate the new savings by subtracting the new expenditure from the new income:
\[ \text{New Savings} = \text{New Income} - \text{New Expenditure} = 8.96x - 5.75x = 3.21x \]

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

### Conclusion
Thus, the increase in savings is \( 0.21x \).