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The problem in the image is about income, tax rates, and changes in income and tax percentages. Let's break down and solve it.

### Problem Statement:
- **Initial Income Decrease**: Shyam's income was decreased by ₹12,500.
- **Tax Rate Changes**: The tax rate increased from 15% to 20%.
- **Ratio of Tax Paid (Before & After)**: The ratio of the tax paid before and after is 2:3.
- **25% Tax-Free Income**: Only 75% of the income is taxable, as 25% is tax-free.

We are asked to find Shyam's initial income.

---

### Let the initial income be **I**.

1. **Tax-Free Portion**: 
   Since 25% of the income is tax-free, the taxable portion of Shyam's income is \( 75\% \) of \( I \), or \( 0.75I \).

2. **Income after Decrease**:
   After a reduction of ₹12,500, the income becomes:
   \[
   I' = I - 12,500
   \]
   The taxable portion of this new income is \( 0.75(I - 12,500) \).

3. **Tax Paid Before and After**:
   - **Before**: Tax rate was 15%, so the tax paid initially was:
     \[
     T_{\text{before}} = 0.15 \times 0.75I = 0.1125I
     \]
   - **After**: Tax rate increased to 20%, so the tax paid now is:
     \[
     T_{\text{after}} = 0.20 \times 0.75(I - 12,500) = 0.15(I - 12,500)
     \]

4. **Given Ratio of Tax Paid**:
   The ratio of tax paid before and after is 2:3, which means:
   \[
   \frac{T_{\text{before}}}{T_{\text{after}}} = \frac{2}{3}
   \]
   Substituting the expressions for \( T_{\text{before}} \) and \( T_{\text{after}} \):
   \[
   \frac{0.1125I}{0.15(I - 12,500)} = \frac{2}{3}
   \]

5. **Solve the Equation**:
   Cross-multiplying to solve for \( I \):
   \[
   3 \times 0.1125I = 2 \times 0.15(I - 12,500)
   \]
   Expanding both sides:
   \[
   0.3375I = 0.30I - 3,750
   \]
   Simplifying further:
   \[
   0.3375I - 0.30I = -3,750
   \]
   \[
   0.0375I = 3,750
   \]
   Solving for \( I \):
   \[
   I = \frac{3,750}{0.0375} = 100,000
   \]

Thus, Shyam's initial income was **₹100,000**.

---

### Answer:
The initial income is **₹100,000**, and none of the options in the list match exactly. Therefore, the correct choice would be **E. None of these**.

---

Let me know if you'd like more details on any part of the solution!

### Related Questions:
1. What would happen if the tax-free income was increased to 30%?
2. How would the result change if the income decrease was ₹15,000 instead of ₹12,500?
3. Can you explain how the taxable portion affects the final tax amount?
4. What if the ratio of tax paid before and after was 3:4 instead of 2:3?
5. How do changes in tax rates typically affect net income?

#### Tip:
Always break down complex problems into smaller parts, focusing on one aspect at a time for clarity.

Income of Shyam was decreased by ₹12,500 while the rate of income tax increased from 15% to 20% and after the tax is 25% of the income tax free. If the ratio of the tax paid before and after is 2:3 respectively, then find the initial income.

This problem demonstrates how to calculate Shyam's initial income and tax obligations after his income decreased by ₹12,500 and his tax rate increased from 15% to 20%, with 25% of the income tax-free. The step-by-step solution explains algebraic manipulation and taxation principles, suitable for students in grades 11-12.

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