By selling an article for 240,a man incurs a loss of 10%. At what price should he sell it, so that he makes a profit of 20%?

Options

A. 264
B. 288
C. 300
D. 320

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the article and then calculate the selling price (SP) required to achieve a profit of 20%.

### Step 1: Determine the Cost Price (CP)
Given that the selling price (SP) is Rs. 240 and there is a loss of 10%, we can use the formula for loss:

\[ \text{Loss} = \text{CP} - \text{SP} \]

Since the loss is 10%, we can express this as:

\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]

Substituting the values:

\[ 240 = \text{CP} \times \left(1 - \frac{10}{100}\right) \]

\[ 240 = \text{CP} \times \left(1 - 0.1\right) \]

\[ 240 = \text{CP} \times 0.9 \]

Now, we can solve for CP:

\[ \text{CP} = \frac{240}{0.9} = \frac{2400}{9} \approx 266.67 \]

### Step 2: Calculate the Selling Price for a 20% Profit
To find the selling price (SP) that gives a profit of 20%, we use the formula for profit:

\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]

Substituting the values we have:

\[ \text{SP} = \frac{2400}{9} \times \left(1 + \frac{20}{100}\right) \]

\[ \text{SP} = \frac{2400}{9} \times 1.2 \]

Calculating this gives:

\[ \text{SP} = \frac{2400 \times 1.2}{9} = \frac{2880}{9} \approx 320 \]

### Final Answer
The selling price at which he should sell the article to make a profit of 20% is **Rs. 320**.

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