The marked price of an article is Rs530. After two successive discounts , it is sold for Rs396.44. If the first discount is 15%, and the second discount is x%, then what is the value of x?

Options

A. 10
B. 15
C. 12
D. 20

Answer

To find the value of \( x \) in the given problem, we will follow these steps:

### Step 1: Calculate the first discount amount
The marked price (MP) of the article is Rs 530. The first discount is 15%.

\[ \text{First Discount} = \frac{15}{100} \times 530 = 79.5 \]

### Step 2: Calculate the price after the first discount
Now, we subtract the first discount from the marked price to find the selling price after the first discount.

\[ \text{Price after First Discount} = 530 - 79.5 = 450.5 \]

### Step 3: Set up the equation for the second discount
Let the second discount be \( x\% \). The selling price after the second discount is given as Rs 396.44.

The amount of the second discount can be expressed as:

\[ \text{Second Discount} = \frac{x}{100} \times 450.5 \]

Thus, the selling price after the second discount can be written as:

\[ \text{Price after Second Discount} = 450.5 - \left(\frac{x}{100} \times 450.5\right) = 396.44 \]

### Step 4: Simplify the equation
We can simplify the equation from Step 3:

\[ 450.5 \left(1 - \frac{x}{100}\right) = 396.44 \]

### Step 5: Solve for \( x \)
Now, we will isolate \( x \):

1. Divide both sides by 450.5:

\[ 1 - \frac{x}{100} = \frac{396.44}{450.5} \]

2. Calculate \( \frac{396.44}{450.5} \):

\[ \frac{396.44}{450.5} \approx 0.88 \]

3. Now, we have:

\[ 1 - \frac{x}{100} = 0.88 \]

4. Rearranging gives:

\[ \frac{x}{100} = 1 - 0.88 = 0.12 \]

5. Multiply both sides by 100:

\[ x = 12 \]

### Conclusion
The value of \( x \) is 12%.

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