The ratio of expenditure and savings of a person is 5 : 3. If the incomeincreases by 20% and the expenditure increases by 10%, then the person’s savings increase by:

Options

A. `36(2)/(3)%`
B. `3(1)/(3)%`
C. `13(1)/(3)%`
D. `30(1)/(3)%`

Answer

To solve the problem step by step, we will follow the given information about the ratio of expenditure and savings, and how they change with the increase in income and expenditure.

### Step 1: Understand the Ratio
The ratio of expenditure to savings is given as 5:3. This means:
- Let the expenditure be \(5x\)
- Let the savings be \(3x\)

### Step 2: Calculate Total Income
Income can be calculated as the sum of expenditure and savings:
\[ \text{Income} = \text{Expenditure} + \text{Savings} = 5x + 3x = 8x \]

### Step 3: Assign a Value to \(x\)
To make calculations easier, we can assign a value to \(x\). Let’s take \(x = 10\):
- Expenditure = \(5x = 5 \times 10 = 50\)
- Savings = \(3x = 3 \times 10 = 30\)
- Income = \(8x = 8 \times 10 = 80\)

### Step 4: Calculate New Income After Increase
The income increases by 20%. Therefore, the new income can be calculated as:
\[ \text{New Income} = \text{Old Income} \times \left(1 + \frac{20}{100}\right) = 80 \times 1.2 = 96 \]

### Step 5: Calculate New Expenditure After Increase
The expenditure increases by 10%. Therefore, the new expenditure can be calculated as:
\[ \text{New Expenditure} = \text{Old Expenditure} \times \left(1 + \frac{10}{100}\right) = 50 \times 1.1 = 55 \]

### Step 6: Calculate New Savings
Now we can find the new savings using the new income and new expenditure:
\[ \text{New Savings} = \text{New Income} - \text{New Expenditure} = 96 - 55 = 41 \]

### Step 7: Calculate Increase in Savings
To find the increase in savings, we subtract the old savings from the new savings:
\[ \text{Increase in Savings} = \text{New Savings} - \text{Old Savings} = 41 - 30 = 11 \]

### Step 8: Calculate Percentage Increase in Savings
Finally, we can calculate the percentage increase in savings:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase in Savings}}{\text{Old Savings}}\right) \times 100 = \left(\frac{11}{30}\right) \times 100 \approx 36.67\% \]

### Conclusion
The person's savings increase by approximately \(36.67\%\).

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