A man spends `2/3rd` of his income. If his income increases by 14% and the expenditure increases by 20%, then the percentage increase in his savings will be

Options

A. `1%`
B. `2%`
C. `4%`
D. `6%`

Answer

To solve the problem step by step, we will first define the variables and then calculate the income, expenditure, and savings before and after the increases.

### Step 1: Define the Income
Let the man's income be represented as \( I \). For simplicity, we can assume:
\[ I = 300x \]

### Step 2: Calculate the Expenditure
The man spends \( \frac{2}{3} \) of his income. Therefore, his expenditure \( E \) can be calculated as:
\[ E = \frac{2}{3} \times I = \frac{2}{3} \times 300x = 200x \]

### Step 3: Calculate the Initial Savings
Savings \( S \) is defined as the difference between income and expenditure:
\[ S = I - E = 300x - 200x = 100x \]

### Step 4: Calculate the New Income after Increase
The income increases by 14%. The new income \( I' \) can be calculated as:
\[ I' = I + 0.14I = 300x + 0.14 \times 300x = 300x + 42x = 342x \]

### Step 5: Calculate the New Expenditure after Increase
The expenditure increases by 20%. The new expenditure \( E' \) can be calculated as:
\[ E' = E + 0.20E = 200x + 0.20 \times 200x = 200x + 40x = 240x \]

### Step 6: Calculate the New Savings
The new savings \( S' \) can be calculated as:
\[ S' = I' - E' = 342x - 240x = 102x \]

### Step 7: Calculate the Increase in Savings
The increase in savings can be calculated as:
\[ \text{Increase in Savings} = S' - S = 102x - 100x = 2x \]

### Step 8: Calculate the Percentage Increase in Savings
The percentage increase in savings can be calculated using the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Savings}}{S} \right) \times 100 = \left( \frac{2x}{100x} \right) \times 100 = 2\% \]

### Final Answer
The percentage increase in his savings is **2%**.

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