The difference between successive discounts of 40% followed by 30% and 45% followed by 20% on the marked price of an article is Rs 12. The marked price of the articles is:

Options

A. Rs 800
B. Rs 400
C. Rs 200
D. Rs 600

Answer

To solve the problem, we need to find the marked price of an article given the difference between successive discounts. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding Successive Discounts**:
We have two sets of successive discounts:
- First set: 40% followed by 30%
- Second set: 45% followed by 20%

2. **Using the Successive Discount Formula**:
The formula for calculating the total discount when two successive discounts are applied is:
\[ \text{Total Discount} = x + y - \left(\frac{x \cdot y}{100}\right) \]
where \(x\) and \(y\) are the percentages of the discounts.

3. **Calculating the Total Discount for the First Set**:
For the first set of discounts (40% and 30%):
- \(x = 40\)
- \(y = 30\)
\[ \text{Total Discount}_1 = 40 + 30 - \left(\frac{40 \cdot 30}{100}\right) \]
\[ = 70 - 12 = 58\% \]

4. **Calculating the Total Discount for the Second Set**:
For the second set of discounts (45% and 20%):
- \(x = 45\)
- \(y = 20\)
\[ \text{Total Discount}_2 = 45 + 20 - \left(\frac{45 \cdot 20}{100}\right) \]
\[ = 65 - 9 = 56\% \]

5. **Finding the Difference Between the Discounts**:
The difference between the two total discounts is:
\[ \text{Difference} = \text{Total Discount}_1 - \text{Total Discount}_2 = 58\% - 56\% = 2\% \]

6. **Setting Up the Equation**:
According to the problem, this difference in percentage corresponds to a monetary difference of Rs 12. Therefore, we can set up the equation:
\[ 2\% \text{ of Marked Price} = 12 \]

7. **Calculating the Marked Price**:
To find the marked price (let's denote it as \(MP\)):
\[ MP = \frac{12}{2\%} = \frac{12}{0.02} = 600 \]

### Conclusion:
The marked price of the article is **Rs 600**.