The difference between a discount of 30% and two successive discounts of 20% and 10% on the marked price of an article is Rs 144. The marked price of the article is:

Options

A. Rs 7,200
B. Rs 7,400
C. Rs 7500
D. Rs 7000

Answer

To solve the problem step by step, we need to find the marked price (MP) of an article given the difference between a single discount and two successive discounts.

### Step-by-Step Solution:

1. **Define the Marked Price (MP)**:
Let the marked price of the article be \( MP \).

2. **Calculate the Single Discount**:
The single discount given is 30%. Therefore, the selling price after the single discount can be calculated as:
\[ \text{Selling Price (SP)} = MP - (30\% \text{ of } MP) = MP \times (1 - 0.30) = MP \times 0.70 \]

3. **Calculate the Successive Discounts**:
The two successive discounts are 20% and 10%. The effective discount can be calculated using the formula for successive discounts:
\[ \text{Effective Discount} = x + y - \left(\frac{x \cdot y}{100}\right) \]
where \( x = 20\% \) and \( y = 10\% \).
\[ \text{Effective Discount} = 20 + 10 - \left(\frac{20 \cdot 10}{100}\right) = 30 - 2 = 28\% \]
Thus, the selling price after the successive discounts is:
\[ \text{SP} = MP - (28\% \text{ of } MP) = MP \times (1 - 0.28) = MP \times 0.72 \]

4. **Set Up the Equation**:
According to the problem, the difference between the selling prices from the two methods is Rs 144:
\[ MP \times 0.70 - MP \times 0.72 = 144 \]
Simplifying this gives:
\[ MP \times (0.70 - 0.72) = 144 \]
\[ MP \times (-0.02) = 144 \]
\[ MP = \frac{144}{-0.02} = 144 \div 0.02 = 7200 \]

5. **Conclusion**:
The marked price of the article is Rs 7200.