The ratio of expenditure and savings is 3 : 2. If the income increases by 15% and the savings increases by 6%, then by how much per cent should his expenditure increases?

Options

A. 25
B. 21
C. 12
D. 24

Answer

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

### Step 1: Understand the given ratio
The ratio of expenditure to savings is given as 3:2. This means if we let the expenditure be \(3x\) and the savings be \(2x\).

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

### Step 3: Assign a value to \(x\)
To simplify calculations, we can assume \(x = 100\). Therefore:
- Expenditure = \(3x = 300\)
- Savings = \(2x = 200\)
- Income = \(5x = 500\)

### Step 4: Calculate the increase in income
The income increases by 15%. So, we calculate 15% of 500:
\[ \text{Increase in Income} = 15\% \text{ of } 500 = \frac{15}{100} \times 500 = 75 \]
Thus, the new income becomes:
\[ \text{New Income} = 500 + 75 = 575 \]

### Step 5: Calculate the increase in savings
The savings increase by 6%. So, we calculate 6% of 200:
\[ \text{Increase in Savings} = 6\% \text{ of } 200 = \frac{6}{100} \times 200 = 12 \]
Thus, the new savings become:
\[ \text{New Savings} = 200 + 12 = 212 \]

### Step 6: Calculate the new expenditure
Since the new income is the sum of new expenditure and new savings, we can find the new expenditure:
\[ \text{New Expenditure} = \text{New Income} - \text{New Savings} = 575 - 212 = 363 \]

### Step 7: Calculate the increase in expenditure
The increase in expenditure is:
\[ \text{Increase in Expenditure} = \text{New Expenditure} - \text{Old Expenditure} = 363 - 300 = 63 \]

### Step 8: Calculate the percentage increase in expenditure
To find the percentage increase in expenditure, we use the formula:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase in Expenditure}}{\text{Old Expenditure}}\right) \times 100 = \left(\frac{63}{300}\right) \times 100 \]
Calculating this gives:
\[ \text{Percentage Increase} = \frac{63 \times 100}{300} = 21\% \]

### Final Answer
The expenditure should increase by **21%**.

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