Subha saves 15% of her income. If her expenditure increases by 20% and savings increase by 60%, then by what percent has her income increased?

Options

A. 26'
B. 35'
C. 24'
D. 30'

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Define Initial Income and Savings
Let Subha's initial income be \( I = 100 \) (this is an arbitrary value that simplifies calculations).

Since she saves 15% of her income:
\[ \text{Initial Savings} = 15\% \text{ of } 100 = 15 \]

### Step 2: Calculate Initial Expenditure
Since income is the sum of savings and expenditure:
\[ \text{Initial Expenditure} = I - \text{Initial Savings} = 100 - 15 = 85 \]

### Step 3: Calculate New Expenditure After Increase
Her expenditure increases by 20%. Therefore, the new expenditure can be calculated as follows:
\[ \text{New Expenditure} = \text{Initial Expenditure} + 20\% \text{ of Initial Expenditure} = 85 + 0.20 \times 85 \]
Calculating the increase:
\[ 0.20 \times 85 = 17 \]
Thus,
\[ \text{New Expenditure} = 85 + 17 = 102 \]

### Step 4: Calculate New Savings After Increase
Her savings increase by 60%. Therefore, the new savings can be calculated as follows:
\[ \text{New Savings} = \text{Initial Savings} + 60\% \text{ of Initial Savings} = 15 + 0.60 \times 15 \]
Calculating the increase:
\[ 0.60 \times 15 = 9 \]
Thus,
\[ \text{New Savings} = 15 + 9 = 24 \]

### Step 5: Calculate New Income
Now, we can find the new income by adding the new savings and new expenditure:
\[ \text{New Income} = \text{New Expenditure} + \text{New Savings} = 102 + 24 = 126 \]

### Step 6: Calculate Increase in Income
The increase in income is:
\[ \text{Increase in Income} = \text{New Income} - \text{Initial Income} = 126 - 100 = 26 \]

### Step 7: Calculate Percentage Increase in Income
Finally, we calculate the percentage increase in income:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Income}}{\text{Initial Income}} \right) \times 100 = \left( \frac{26}{100} \right) \times 100 = 26\% \]

### Final Answer:
Subha's income has increased by **26%**.

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