The marked price of an article is ₹2,560. During a sale. two sucessive discounts of 20% and `x%` are offered on it. If the selling price of the article is ₹1,679.36, the the value of x is:

Options

A. 16.5
B. 12.5
C. 15
D. 18

Answer

To solve the problem, we need to find the value of \( x \) given the marked price, the successive discounts, and the selling price.

### Step 1: Calculate the price after the first discount
The marked price of the article is ₹2,560. The first discount is 20%.

To find the price after the first discount, we can calculate:
\[ \text{Price after first discount} = \text{Marked Price} - \left( \text{Marked Price} \times \frac{20}{100} \right) \]

Calculating the first discount:
\[ \text{First Discount} = 2560 \times 0.20 = 512 \]

Now, subtract the discount from the marked price:
\[ \text{Price after first discount} = 2560 - 512 = 2048 \]

### Step 2: Calculate the price after the second discount
Let the second discount be \( x\% \). The price after the second discount can be expressed as:
\[ \text{Selling Price} = \text{Price after first discount} - \left( \text{Price after first discount} \times \frac{x}{100} \right) \]

Substituting the known values:
\[ 1679.36 = 2048 - \left( 2048 \times \frac{x}{100} \right) \]

### Step 3: Rearranging the equation
Rearranging the equation to isolate \( x \):
\[ 1679.36 = 2048 - \frac{2048x}{100} \]
\[ \frac{2048x}{100} = 2048 - 1679.36 \]
\[ \frac{2048x}{100} = 368.64 \]

### Step 4: Solve for \( x \)
Now, multiply both sides by 100 to eliminate the fraction:
\[ 2048x = 36864 \]

Next, divide both sides by 2048:
\[ x = \frac{36864}{2048} = 18 \]

Thus, the value of \( x \) is \( 18\% \).

### Final Answer
The value of \( x \) is \( 18\% \).

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