A man's annual income has increased by `Rs.2` lakh but the tax on income that he has to pay has reduced from `25%` to `20%`. He now pays the same amount of tax as before. What is the increased income (in lakhs) ?

Options

A. `10` lakh
B. `20` lakh
C. `5` lakh
D. `15` lakh

Answer

To solve the problem step by step, let's break down the information given and set up the equations accordingly.

### Step 1: Define the variables
Let the man's original annual income be \( x \) lakhs.

### Step 2: Determine the new income
After the increase, his new income will be:
\[ x + 2 \text{ lakhs} \]

### Step 3: Calculate the tax before and after the increase
- Before the increase, the tax he paid was \( 25\% \) of his original income:
\[ \text{Tax before} = 0.25x \]

- After the increase, the tax he pays is \( 20\% \) of his new income:
\[ \text{Tax after} = 0.20(x + 2) \]

### Step 4: Set up the equation
According to the problem, the amount of tax he pays now is the same as before:
\[ 0.25x = 0.20(x + 2) \]

### Step 5: Solve the equation
1. Distribute the \( 0.20 \):
\[ 0.25x = 0.20x + 0.40 \]

2. Rearrange the equation to isolate \( x \):
\[ 0.25x - 0.20x = 0.40 \]
\[ 0.05x = 0.40 \]

3. Divide both sides by \( 0.05 \):
\[ x = \frac{0.40}{0.05} = 8 \text{ lakhs} \]

### Step 6: Calculate the increased income
Now that we have the original income \( x \), we can find the increased income:
\[ \text{Increased income} = x + 2 = 8 + 2 = 10 \text{ lakhs} \]

### Final Answer
The increased income is \( 10 \) lakhs.

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