On selling an article for Rs 195, a shopkeeper losses `35%`. At what price (in Rs) he should sell the article in order to earn a profit of `30%`?

Options

A. 95
B. 100
C. 390
D. 280

Answer

To solve the problem step by step, we will first determine the cost price of the article based on the given selling price and loss percentage. Then, we will calculate the selling price needed to achieve a profit of 30%.

### Step 1: Determine the Cost Price
Let the cost price (CP) of the article be represented as \( CP = 100x \).

Given that the shopkeeper sells the article for Rs. 195 and incurs a loss of 35%, we can express the selling price (SP) in terms of the cost price:
\[ SP = CP - \text{Loss} \]
The loss can be calculated as:
\[ \text{Loss} = 35\% \text{ of } CP = 0.35 \times CP = 0.35 \times 100x = 35x \]
Thus, we can write:
\[ SP = 100x - 35x = 65x \]
We know that the selling price is Rs. 195, so we can set up the equation:
\[ 65x = 195 \]

### Step 2: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 65:
\[ x = \frac{195}{65} = 3 \]

### Step 3: Calculate the Cost Price
Now that we have \( x \), we can find the cost price:
\[ CP = 100x = 100 \times 3 = 300 \]

### Step 4: Determine the Selling Price for a Profit of 30%
To find the selling price that would yield a profit of 30%, we first calculate the desired selling price (SP) using the formula:
\[ SP = CP + \text{Profit} \]
The profit can be calculated as:
\[ \text{Profit} = 30\% \text{ of } CP = 0.30 \times CP = 0.30 \times 300 = 90 \]
Thus, the selling price for a profit of 30% is:
\[ SP = CP + \text{Profit} = 300 + 90 = 390 \]

### Final Answer
The shopkeeper should sell the article for **Rs. 390** to earn a profit of 30%.

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