Lalit purchased an article from a shopkeeper who allowed a discount of `30%` on the marked price of the article but charged a sales tax of `25%` on the discounted price. Lalit then sold the article to Puray for 1323 and thereby earned a profit of `40%` on his cost price. What is the marked price of the article?

Options

A. ₹ 1180
B. ₹ 1080
C. ₹ 1040
D. ₹ 1160

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define the Marked Price
Let the marked price of the article be \( M \).

### Step 2: Calculate the Discounted Price
Lalit receives a discount of 30% on the marked price. Therefore, the discounted price \( D \) can be calculated as:
\[ D = M - 0.30M = 0.70M \]

### Step 3: Calculate the Selling Price Including Sales Tax
Lalit is charged a sales tax of 25% on the discounted price. Therefore, the selling price \( S \) that Lalit pays can be calculated as:
\[ S = D + 0.25D = 1.25D = 1.25 \times 0.70M = 0.875M \]

### Step 4: Determine the Cost Price
We know that Lalit sold the article to Puray for ₹1323 and earned a profit of 40% on his cost price. Let the cost price \( C \) be represented as:
\[ C = S \]
Since Lalit sold the article for ₹1323, we can express this as:
\[ Selling Price = Cost Price + Profit \]
Given that the profit is 40% of the cost price, we can write:
\[ 1323 = C + 0.40C = 1.40C \]
Thus, we can find the cost price \( C \):
\[ C = \frac{1323}{1.40} = 945 \]

### Step 5: Relate Cost Price to Discounted Price
From Step 3, we know that the cost price \( C \) is equal to the selling price \( S \):
\[ C = 0.875M \]
Substituting the value of \( C \):
\[ 945 = 0.875M \]

### Step 6: Solve for Marked Price
Now, we can solve for \( M \):
\[ M = \frac{945}{0.875} \]
Calculating this gives:
\[ M = 1080 \]

### Conclusion
Thus, the marked price of the article is ₹1080.

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