By selling a shirt for Rs. 285 a shopkeeper loses 5%. At what price should he sell the shirt so as to gain 15% ?

Answer

To solve the problem step by step, we will first determine the cost price of the shirt based on the given selling price and loss percentage. Then, we will calculate the new selling price required to achieve a 15% profit.

### Step 1: Determine the Cost Price (CP)
We know that the selling price (SP) is Rs. 285 and the shopkeeper incurs a loss of 5%.

Using the formula for loss:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \]
Since the loss is 5%, we can express this as:
\[ \text{Selling Price} = \text{Cost Price} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
Substituting the values we have:
\[ 285 = \text{CP} \times \left(1 - \frac{5}{100}\right) \]
\[ 285 = \text{CP} \times 0.95 \]
Now, solving for CP:
\[ \text{CP} = \frac{285}{0.95} = 300 \]

### Step 2: Calculate the New Selling Price for a 15% Profit
Now that we have the cost price (CP) as Rs. 300, we need to find the selling price (SP) that would give a 15% profit.

Using the formula for profit:
\[ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]
Substituting the values:
\[ \text{SP} = 300 \times \left(1 + \frac{15}{100}\right) \]
\[ \text{SP} = 300 \times 1.15 = 345 \]

### Final Answer
The shopkeeper should sell the shirt for Rs. 345 to gain a 15% profit.

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