When an article is sold for rs 291, then is a loss of 3%. What will be the selling price of the article. If it is sold at a gain of 8% ?

Options

A. rs 308
B. rs 332
C. rs 324
D. rs 316

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article first and then calculate the selling price (SP) when there is a gain of 8%.

### Step 1: Understand the relationship between cost price, selling price, and loss percentage.
When there is a loss of 3%, the relationship between the cost price (CP) and selling price (SP) can be expressed as:
\[ \text{SP} = \text{CP} - \text{Loss} \]
Given that the loss is 3%, we can express this as:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{3}{100}\right) = \text{CP} \times \frac{97}{100} \]

### Step 2: Set up the equation using the given selling price.
According to the problem, when the article is sold for Rs. 291, there is a loss of 3%. Therefore, we can set up the equation:
\[ 291 = \text{CP} \times \frac{97}{100} \]

### Step 3: Solve for the cost price (CP).
To find the cost price (CP), rearrange the equation:
\[ \text{CP} = 291 \times \frac{100}{97} \]
Calculating this gives:
\[ \text{CP} = 291 \times 1.03092783505 \approx 300 \]

### Step 4: Calculate the selling price (SP) at a gain of 8%.
Now, we need to find the selling price when there is a gain of 8%. The relationship can be expressed as:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{8}{100}\right) = \text{CP} \times \frac{108}{100} \]

### Step 5: Substitute the value of CP into the selling price equation.
Substituting the value of CP we found:
\[ \text{SP} = 300 \times \frac{108}{100} \]
Calculating this gives:
\[ \text{SP} = 300 \times 1.08 = 324 \]

### Conclusion:
The selling price of the article if it is sold at a gain of 8% is Rs. 324.

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