When income of a man increased by `Rs.6` lakhs then tax rate reduced from `18%` to `15%` . While in both the situation `25%` of incomes is tax free. Then find his present income if he paid equal tax in both cases.

Options

A. `36` lakh
B. `40` lakh
C. `25` lakh
D. `45` lakh

Answer

To solve the problem, we need to set up equations based on the information provided. Let's break it down step by step.

### Step 1: Define the variables
Let the present income of the man be \( X + 6 \) lakhs, where \( X \) is his previous income in lakhs.

### Step 2: Calculate the taxable income
Since 25% of the income is tax-free, the taxable income can be calculated as follows:
- For the previous income \( X \):
\[ \text{Taxable Income (Old)} = X - 0.25X = 0.75X \]
- For the present income \( X + 6 \):
\[ \text{Taxable Income (New)} = (X + 6) - 0.25(X + 6) = 0.75(X + 6) \]

### Step 3: Set up the tax equations
Now we can set up the equations for the tax paid in both cases:
- Tax paid on old income at 18%:
\[ \text{Tax (Old)} = 0.18 \times 0.75X = 0.135X \]
- Tax paid on new income at 15%:
\[ \text{Tax (New)} = 0.15 \times 0.75(X + 6) = 0.1125(X + 6) \]

### Step 4: Set the taxes equal
According to the problem, the tax paid in both cases is equal:
\[ 0.135X = 0.1125(X + 6) \]

### Step 5: Solve the equation
Now, we will solve for \( X \):
1. Expand the right side:
\[ 0.135X = 0.1125X + 0.675 \]
2. Rearrange the equation:
\[ 0.135X - 0.1125X = 0.675 \]
\[ 0.0225X = 0.675 \]
3. Divide both sides by 0.0225:
\[ X = \frac{0.675}{0.0225} = 30 \]

### Step 6: Calculate the present income
Now that we have \( X \), we can find the present income:
\[ \text{Present Income} = X + 6 = 30 + 6 = 36 \text{ lakhs} \]

### Final Answer
The present income of the man is **36 lakhs**.

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