On selling an article for Rs. 360 , a shopkeeper losses `10%` . For how much (in Rs. ) he should sell the article in order to earn a profit of `25%` ?

Options

A. A)250
B. B)500
C. C)260
D. D)420

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the article based on the selling price (SP) and the loss percentage. Then, we will calculate the new selling price required to achieve a profit of 25%.

### Step 1: Determine the Cost Price (CP)
Given that the selling price (SP1) is Rs. 360 and the shopkeeper incurs a loss of 10%, we can express this mathematically.

Loss of 10% means that the selling price is 90% of the cost price. Therefore, we can write:
\[ SP1 = CP \times \left(1 - \frac{10}{100}\right) \]
\[ 360 = CP \times 0.90 \]

### Step 2: Solve for CP
To find the cost price (CP), we can rearrange the equation:
\[ CP = \frac{360}{0.90} \]
Calculating this gives:
\[ CP = 400 \]

### Step 3: Determine the Selling Price for 25% Profit
Now that we have the cost price, we need to find the selling price (SP2) that would give a profit of 25%.

A profit of 25% means that the selling price is 125% of the cost price. Therefore, we can express this as:
\[ SP2 = CP \times \left(1 + \frac{25}{100}\right) \]
\[ SP2 = 400 \times 1.25 \]

### Step 4: Calculate SP2
Now, we calculate:
\[ SP2 = 400 \times 1.25 = 500 \]

Thus, the shopkeeper should sell the article for Rs. 500 in order to earn a profit of 25%.

### Final Answer
The selling price to earn a profit of 25% is Rs. 500.

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