If the difference between the selling prices of an article, when sold at 22% discount and at 14.5% discount, is Rs 285, then the marked price of the article is:

Options

A. Rs 3,400
B. Rs 3,500
C. Rs 3,800
D. Rs 2,800

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 the variables
Let the marked price of the article be \( M \).

### Step 2: Calculate the selling prices
The selling price when sold at a 22% discount can be calculated as:
\[ \text{Selling Price at 22% discount} = M - (22\% \text{ of } M) = M - 0.22M = 0.78M \]

The selling price when sold at a 14.5% discount can be calculated as:
\[ \text{Selling Price at 14.5% discount} = M - (14.5\% \text{ of } M) = M - 0.145M = 0.855M \]

### Step 3: Set up the equation for the difference in selling prices
According to the problem, the difference between the two selling prices is Rs 285:
\[ 0.855M - 0.78M = 285 \]

### Step 4: Simplify the equation
Now, simplify the left side:
\[ 0.855M - 0.78M = 0.075M \]
So, we have:
\[ 0.075M = 285 \]

### Step 5: Solve for \( M \)
To find \( M \), divide both sides by 0.075:
\[ M = \frac{285}{0.075} \]
Calculating this gives:
\[ M = 3800 \]

### Conclusion
The marked price of the article is Rs 3800.

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