After giving two successive discounts, a shirt with a marked price of ₹ 200 is available at ₹ 100. If the second discount is 20%, then the first discount is

Answer

To solve the problem, we need to find the first discount percentage (d1) given that the marked price (MP) of the shirt is ₹200, the selling price (SP) after two successive discounts is ₹100, and the second discount (d2) is 20%.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Marked Price (MP) = ₹200
- Selling Price (SP) = ₹100
- Second Discount (d2) = 20%

2. **Calculate the Net Discount:**
- The net discount can be calculated using the formula:
\[ \text{Net Discount} = \frac{\text{MP} - \text{SP}}{\text{MP}} \times 100 \]
- Substituting the values:
\[ \text{Net Discount} = \frac{200 - 100}{200} \times 100 = \frac{100}{200} \times 100 = 50\% \]

3. **Use the Net Discount Formula:**
- The formula for net discount when there are two successive discounts is:
\[ \text{Net Discount} = d1 + d2 - \frac{d1 \times d2}{100} \]
- We know the net discount is 50%, and d2 is 20%. Substituting these values:
\[ 50 = d1 + 20 - \frac{d1 \times 20}{100} \]

4. **Rearranging the Equation:**
- Rearranging gives:
\[ 50 = d1 + 20 - \frac{d1}{5} \]
- This simplifies to:
\[ 50 = d1 + 20 - 0.2d1 \]
\[ 50 = 0.8d1 + 20 \]

5. **Isolate d1:**
- Subtract 20 from both sides:
\[ 30 = 0.8d1 \]
- Now, divide both sides by 0.8:
\[ d1 = \frac{30}{0.8} = 37.5 \]

6. **Conclusion:**
- The first discount (d1) is 37.5%.

### Final Answer:
The first discount is **37.5%**.