Oniselling an article for ₹ 240, a trader loses `4%`. In order to gain `10%` he must sell that article for:

Options

A. ₹ 275
B. ₹ 340
C. ₹ 320
D. ₹ 2664

Answer

To solve the problem step by step, we need to find the cost price of the article first, and then determine the selling price required to achieve a 10% profit.

### Step 1: Determine the Cost Price (CP)
Given that the selling price (SP) is ₹240 and the trader incurs a loss of 4%, we can use the formula for selling price in terms of cost price and loss percentage:

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

Substituting the known values:

\[ 240 = CP \times \left(1 - \frac{4}{100}\right) \]

This simplifies to:

\[ 240 = CP \times 0.96 \]

Now, we can solve for CP:

\[ CP = \frac{240}{0.96} = 250 \]

### Step 2: Calculate the Selling Price for a 10% Profit
Now that we have the cost price (CP = ₹250), we need to find the selling price (SP) that would yield a 10% profit. The formula for selling price in terms of cost price and profit percentage is:

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

Substituting the values we have:

\[ SP = 250 \times \left(1 + \frac{10}{100}\right) \]

This simplifies to:

\[ SP = 250 \times 1.10 = 275 \]

### Final Answer
The selling price required to gain a 10% profit is ₹275.

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