An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article ?

Options

A. Rs. 520
B. Rs. 480
C. Rs. 460
D. Rs. 500

Answer

To find the marked price of an article sold for Rs. 288 after successive discounts of 20% and 25%, we can follow these steps:

### Step 1: Understand the Discounts
The article is sold after two successive discounts:
- The first discount (D1) is 20%, which can be represented as a fraction: \( \frac{20}{100} = \frac{1}{5} \).
- The second discount (D2) is 25%, which can be represented as a fraction: \( \frac{25}{100} = \frac{1}{4} \).

### Step 2: Calculate the Selling Price after Discounts
If the marked price (MP) is denoted as \( x \):
1. After the first discount of 20%, the selling price becomes:
\[ \text{Selling Price after D1} = x - 0.2x = 0.8x \]
2. After applying the second discount of 25% on the new price:
\[ \text{Selling Price after D2} = 0.8x - 0.25(0.8x) = 0.8x \times (1 - 0.25) = 0.8x \times 0.75 = 0.6x \]

### Step 3: Set up the Equation
We know that the final selling price after both discounts is Rs. 288. Therefore:
\[ 0.6x = 288 \]

### Step 4: Solve for the Marked Price (MP)
To find \( x \), we rearrange the equation:
\[ x = \frac{288}{0.6} \]
Calculating this gives:
\[ x = \frac{288 \times 10}{6} = \frac{2880}{6} = 480 \]

### Conclusion
The marked price of the article is Rs. 480.

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