Madan pays income tax at the rate of 10%. If his income is increased by 10% and his tax rate increases to 15%, then his net income after paying tax would increase by ₹ 350.What is Madan's income?

Options

A. ₹ 8,000
B. ₹ 10,000
C. ₹ 12,000
D. ₹ 14,000

Answer

To find Madan's income, we will follow these steps:

### Step 1: Define Madan's initial income
Let Madan's initial income be \( x \).

### Step 2: Calculate the initial net income after tax
Madan pays income tax at the rate of 10%. Therefore, his net income after paying tax can be calculated as:
\[ \text{Net Income} = x - 0.10x = 0.90x = \frac{9x}{10} \]

### Step 3: Calculate the new income after a 10% increase
If Madan's income is increased by 10%, his new income will be:
\[ \text{New Income} = x + 0.10x = 1.10x = \frac{11x}{10} \]

### Step 4: Calculate the new net income after a 15% tax
With the new income, the tax rate increases to 15%. Thus, his new net income after tax will be:
\[ \text{New Net Income} = \text{New Income} - 0.15 \times \text{New Income} = 1.10x - 0.15 \times 1.10x = 1.10x \times (1 - 0.15) = 1.10x \times 0.85 = 0.935x \]

### Step 5: Set up the equation based on the increase in net income
According to the problem, the increase in net income is ₹350. Therefore, we can set up the equation:
\[ \text{New Net Income} - \text{Old Net Income} = 350 \]
Substituting the values we calculated:
\[ 0.935x - 0.90x = 350 \]

### Step 6: Simplify the equation
Now, simplify the left side:
\[ 0.935x - 0.90x = 0.035x \]
So, we have:
\[ 0.035x = 350 \]

### Step 7: Solve for \( x \)
To find \( x \), divide both sides by 0.035:
\[ x = \frac{350}{0.035} \]
Calculating this gives:
\[ x = 10000 \]

### Conclusion
Madan's income is ₹10,000.

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