A man's annual income has increased by 4.5 lakhs but tax rate on income that he to pay has reduced from 26% to 20%. He now pays 12000 more income tax. What is his increased income (in lakhs)?

Options

A. 17.5 lakh
B. 15.5 lakh
C. 18.5 lakh
D. 16.51 lakh

Answer

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

### Step 1: Define the Variables
Let the original income of the man be \( x \) lakhs.

### Step 2: Calculate the Original Tax
The original tax he paid was 26% of his income:
\[ \text{Original Tax} = \frac{26}{100} \times x = 0.26x \text{ lakhs} \]

### Step 3: Calculate the New Income
His income has increased by 4.5 lakhs, so his new income is:
\[ \text{New Income} = x + 4.5 \text{ lakhs} \]

### Step 4: Calculate the New Tax
The new tax he pays is 20% of his new income:
\[ \text{New Tax} = \frac{20}{100} \times (x + 4.5) = 0.20(x + 4.5) \text{ lakhs} \]

### Step 5: Set Up the Equation
According to the problem, the new tax is 12,000 more than the original tax. We can express this as:
\[ 0.20(x + 4.5) = 0.26x + 12 \]

### Step 6: Simplify the Equation
Expanding the left side:
\[ 0.20x + 0.90 = 0.26x + 12 \]

### Step 7: Rearranging the Equation
Now, move all terms involving \( x \) to one side and constant terms to the other side:
\[ 0.20x - 0.26x = 12 - 0.90 \]
\[ -0.06x = 11.10 \]

### Step 8: Solve for \( x \)
Dividing both sides by -0.06:
\[ x = \frac{11.10}{0.06} = 185 \text{ lakhs} \]

### Step 9: Calculate the Increased Income
Now, we need to find the increased income:
\[ \text{Increased Income} = x + 4.5 = 185 + 4.5 = 189.5 \text{ lakhs} \]

### Final Answer
Thus, the increased income is:
\[ \text{Increased Income} = 189.5 \text{ lakhs} \]

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