An article is sold for ₹680 after two successive discounts of 20% and x% on its marked price. The marked price of the article is ₹1,000. What is the value of x?

Options

A. 15
B. 15.5
C. 12.5
D. 16

Answer

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

### Step 1: Identify the Marked Price and Discounts
The marked price of the article is given as ₹1000. The first discount is 20%.

### Step 2: Calculate the First Discount
To calculate the first discount:
\[ \text{First Discount} = \text{Marked Price} \times \frac{20}{100} = 1000 \times 0.20 = ₹200 \]

### Step 3: Calculate the Price After First Discount
Subtract the first discount from the marked price:
\[ \text{Price after First Discount} = \text{Marked Price} - \text{First Discount} = 1000 - 200 = ₹800 \]

### Step 4: Set Up the Equation for the Second Discount
Let \( x \) be the percentage of the second discount. The selling price after the second discount is given as ₹680. Therefore, we can write:
\[ \text{Selling Price} = \text{Price after First Discount} - \text{Second Discount} \]
\[ 680 = 800 - \left(800 \times \frac{x}{100}\right) \]

### Step 5: Solve for the Second Discount
Rearranging the equation:
\[ 800 \times \frac{x}{100} = 800 - 680 \]
\[ 800 \times \frac{x}{100} = 120 \]

### Step 6: Isolate \( x \)
To find \( x \):
\[ \frac{x}{100} = \frac{120}{800} \]
\[ x = \frac{120}{800} \times 100 \]
\[ x = \frac{12000}{800} = 15 \]

### Conclusion
The value of \( x \) is \( 15\% \).

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