A shopkeeper allows two successive discounts of 20% and 10% on selling an article. If he gets Rs 432 for the article, then what is the marked price (in Rs) of the article?

Options

A. 650
B. 600
C. 580
D. 620

Answer

To find the marked price of the article after applying two successive discounts of 20% and 10%, we can follow these steps:

### Step 1: Calculate the net discount
The formula for calculating the net discount when two successive discounts \( A \) and \( B \) are applied is:
\[ \text{Net Discount} = A + B - \left(\frac{A \times B}{100}\right) \]
Here, \( A = 20\% \) and \( B = 10\% \).

### Step 2: Substitute the values into the formula
Substituting the values into the formula gives:
\[ \text{Net Discount} = 20 + 10 - \left(\frac{20 \times 10}{100}\right) \]
Calculating the multiplication:
\[ 20 \times 10 = 200 \]
Now, divide by 100:
\[ \frac{200}{100} = 2 \]
So, the net discount becomes:
\[ \text{Net Discount} = 20 + 10 - 2 = 28\% \]

### Step 3: Calculate the selling price after discount
If the marked price is \( M \), then after a net discount of 28%, the selling price \( SP \) can be expressed as:
\[ SP = M \times \left(1 - \frac{\text{Net Discount}}{100}\right) \]
Substituting the net discount:
\[ SP = M \times \left(1 - \frac{28}{100}\right) = M \times 0.72 \]

### Step 4: Set up the equation with the selling price
We know that the selling price \( SP \) is Rs 432. Therefore, we have:
\[ 432 = M \times 0.72 \]

### Step 5: Solve for the marked price \( M \)
To find \( M \), rearrange the equation:
\[ M = \frac{432}{0.72} \]
Calculating the division:
\[ M = 600 \]

### Final Answer
The marked price of the article is Rs 600.

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