If the difference between the selling price of an article when sold at `18%` discount and at `10.5%` discount is Rs. 192 then the marked price of the article is

Options

A. Rs. 2, 580
B. Rs. 2, 480
C. Rs. 2, 560
D. Rs. 2, 500

Answer

To find the marked price of the article based on the given discounts and the difference in selling prices, we can follow these steps:

### Step 1: Define Variables
Let the marked price of the article be denoted as \( MP \).

### Step 2: Calculate Selling Prices
The selling price when sold at an 18% discount can be calculated as:
\[ SP_{18\%} = MP - (18\% \text{ of } MP) = MP - 0.18 \times MP = 0.82 \times MP \]

The selling price when sold at a 10.5% discount can be calculated as:
\[ SP_{10.5\%} = MP - (10.5\% \text{ of } MP) = MP - 0.105 \times MP = 0.895 \times MP \]

### Step 3: Set Up the Equation
According to the problem, the difference between these two selling prices is Rs. 192:
\[ SP_{10.5\%} - SP_{18\%} = 192 \]
Substituting the expressions we derived:
\[ 0.895 \times MP - 0.82 \times MP = 192 \]

### Step 4: Simplify the Equation
Now, simplify the left side:
\[ (0.895 - 0.82) \times MP = 192 \]
\[ 0.075 \times MP = 192 \]

### Step 5: Solve for Marked Price
To find \( MP \), divide both sides by 0.075:
\[ MP = \frac{192}{0.075} \]
Calculating this gives:
\[ MP = 2560 \]

### Conclusion
The marked price of the article is Rs. 2560.

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