On selling an article for ruppees 7200, a person loses 36.66% of its selling price. At what price should be sell it to gain 25% on its cost price ?

Options

A. 13120
B. 11890
C. 10250
D. 12300

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article first, then determine the selling price (SP) required to achieve a 25% gain on the cost price.

### Step 1: Understand the Loss Percentage
The person sells the article for Rs. 7200 and incurs a loss of 36.66% on the selling price.

### Step 2: Calculate the Loss in Rupees
To find the loss in rupees, we can use the formula:
\[ \text{Loss} = \text{Selling Price} \times \frac{\text{Loss Percentage}}{100} \]
Substituting the values:
\[ \text{Loss} = 7200 \times \frac{36.66}{100} = 7200 \times 0.3666 = 2639.52 \]

### Step 3: Calculate the Cost Price
The cost price can be calculated using the formula:
\[ \text{Cost Price} = \text{Selling Price} + \text{Loss} \]
Substituting the values:
\[ \text{Cost Price} = 7200 + 2639.52 = 9839.52 \]

### Step 4: Calculate the Selling Price for 25% Gain
To find the selling price for a 25% gain on the cost price, we use the formula:
\[ \text{Selling Price} = \text{Cost Price} + \left(\text{Cost Price} \times \frac{Gain Percentage}{100}\right) \]
Substituting the values:
\[ \text{Selling Price} = 9839.52 + \left(9839.52 \times \frac{25}{100}\right) \]
\[ \text{Selling Price} = 9839.52 + 2459.88 = 12299.40 \]

### Final Answer
The selling price at which the article should be sold to gain 25% on its cost price is **Rs. 12299.40**.

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