Manoj used to spend 33% of his income on food. He got an increment of Rs 1000 but did not increase his expenditure on food items. As a result his expenditure on food dropped to 27%. What was initial volume

Options

A. Rs 5500
B. Rs 6500
C. Rs 5000
D. Rs 4500

Answer

To solve the problem step by step, let's denote Manoj's initial income as \( X \).

### Step 1: Define the initial income and expenditure
Let:
- Initial income = \( X \)
- Initial expenditure on food = 33% of \( X \) = \( 0.33X \)

### Step 2: Define the new income after the increment
After receiving an increment of Rs 1000, his new income becomes:
- New income = \( X + 1000 \)

### Step 3: Define the new expenditure on food
After the increment, his expenditure on food drops to 27% of his new income:
- New expenditure on food = 27% of \( (X + 1000) \) = \( 0.27(X + 1000) \)

### Step 4: Set up the equation
Since his expenditure on food did not change, we can equate the initial expenditure to the new expenditure:
\[ 0.33X = 0.27(X + 1000) \]

### Step 5: Expand and simplify the equation
Expanding the right side:
\[ 0.33X = 0.27X + 270 \]

### Step 6: Rearrange the equation
Subtract \( 0.27X \) from both sides:
\[ 0.33X - 0.27X = 270 \]
\[ 0.06X = 270 \]

### Step 7: Solve for \( X \)
Now, divide both sides by 0.06:
\[ X = \frac{270}{0.06} = 4500 \]

### Conclusion
Manoj's initial income was Rs 4500.

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