Madan spends `50%` of his income on house hold expenditure and `60%` of the remaining on personal expenditure. Of the remaining, he pays `50%` towards income tax and saves the reamining Rs. 1200. What is the personal expenditure of Madan?

Options

A. Rs. 1800
B. Rs. 2400
C. Rs. 3600
D. Rs. 4800

Explanation

To find Madan's personal expenditure, we will break down the problem step by step.

### Step 1: Define Madan's Income
Let Madan's total income be represented as \( 100x \).

### Step 2: Calculate Household Expenditure
Madan spends \( 50\% \) of his income on household expenditure:
\[ \text{Household Expenditure} = 50\% \text{ of } 100x = \frac{50}{100} \times 100x = 50x \]

### Step 3: Calculate Remaining Income After Household Expenditure
After spending on household expenditure, the remaining income is:
\[ \text{Remaining Income} = 100x - 50x = 50x \]

### Step 4: Calculate Personal Expenditure
Madan spends \( 60\% \) of the remaining income on personal expenditure:
\[ \text{Personal Expenditure} = 60\% \text{ of } 50x = \frac{60}{100} \times 50x = 30x \]

### Step 5: Calculate Remaining Income After Personal Expenditure
After personal expenditure, the remaining income is:
\[ \text{Remaining Income} = 50x - 30x = 20x \]

### Step 6: Calculate Income Tax
Madan pays \( 50\% \) of the remaining income towards income tax:
\[ \text{Income Tax} = 50\% \text{ of } 20x = \frac{50}{100} \times 20x = 10x \]

### Step 7: Calculate Remaining Income After Income Tax
The remaining income after paying income tax is:
\[ \text{Remaining Income} = 20x - 10x = 10x \]

### Step 8: Relate Remaining Income to Savings
We know that this remaining income is equal to his savings of Rs. 1200:
\[ 10x = 1200 \]

### Step 9: Solve for \( x \)
To find \( x \), divide both sides by 10:
\[ x = \frac{1200}{10} = 120 \]

### Step 10: Calculate Personal Expenditure
Now that we have \( x \), we can find Madan's personal expenditure:
\[ \text{Personal Expenditure} = 30x = 30 \times 120 = 3600 \]

### Final Answer
Madan's personal expenditure is Rs. 3600.

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