A tax payer is exempted of income tax for the first 100000 of his annual income but for the rest of the income, he has to pay a tax at the rate of 20%. If he paid 3160 as income tax for a year, his monthly income is

Options

A. 11580
B. 103160
C. 13610
D. 9650

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript:

### Step 1: Define the Annual Income
Let the annual income be represented as \( x \).

### Step 2: Determine the Taxable Income
According to the problem, the first ₹100,000 of income is exempt from tax. Therefore, the taxable income is \( x - 100,000 \).

### Step 3: Calculate the Tax Paid
The tax rate on the taxable income is 20%. Thus, the tax paid can be expressed as:
\[ \text{Tax Paid} = 20\% \text{ of } (x - 100,000) = \frac{20}{100} \times (x - 100,000) \]
This is given to be ₹3160.

### Step 4: Set Up the Equation
We can set up the equation based on the information provided:
\[ \frac{20}{100} \times (x - 100,000) = 3160 \]

### Step 5: Simplify the Equation
To simplify, we can multiply both sides by 100 to eliminate the fraction:
\[ 20 \times (x - 100,000) = 3160 \times 100 \]
This simplifies to:
\[ 20 \times (x - 100,000) = 316000 \]

### Step 6: Divide Both Sides by 20
Now, divide both sides by 20:
\[ x - 100,000 = \frac{316000}{20} \]
Calculating the right side gives:
\[ x - 100,000 = 15800 \]

### Step 7: Solve for \( x \)
Now, add ₹100,000 to both sides to find \( x \):
\[ x = 100,000 + 15800 \]
Calculating this gives:
\[ x = 115800 \]

### Step 8: Calculate Monthly Income
To find the monthly income, divide the annual income by 12:
\[ \text{Monthly Income} = \frac{115800}{12} \]
Calculating this gives:
\[ \text{Monthly Income} = 9650 \]

### Final Answer
Thus, the monthly income of the taxpayer is ₹9650.

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