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

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the given values
- Selling Price (SP) = Rs. 285
- Loss Percentage = 5%
- Gain Percentage = 15%

### Step 2: Calculate the Cost Price (CP)
Since the shopkeeper incurs a loss of 5%, we can express the relationship between CP and SP as follows:
\[ \text{SP} = \text{CP} - \left( \frac{\text{Loss Percentage}}{100} \times \text{CP} \right) \]

Substituting the known values:
\[ 285 = \text{CP} - \left( \frac{5}{100} \times \text{CP} \right) \]

This can be rewritten as:
\[ 285 = \text{CP} - \frac{5}{100} \text{CP} \]
\[ 285 = \text{CP} \left( 1 - \frac{5}{100} \right) \]
\[ 285 = \text{CP} \left( \frac{95}{100} \right) \]

Now, we can solve for CP:
\[ \text{CP} = 285 \times \frac{100}{95} \]
\[ \text{CP} = 285 \times \frac{20}{19} \]
\[ \text{CP} = 300 \text{ Rs.} \]

### Step 3: Calculate the new Selling Price for a 15% gain
To find the new selling price (SP) for a gain of 15%, we can use the formula:
\[ \text{New SP} = \text{CP} + \left( \frac{\text{Gain Percentage}}{100} \times \text{CP} \right) \]

Substituting the known values:
\[ \text{New SP} = 300 + \left( \frac{15}{100} \times 300 \right) \]
\[ \text{New SP} = 300 + 45 \]
\[ \text{New SP} = 345 \text{ Rs.} \]

### Final Answer:
The shopkeeper should sell the tie for Rs. 345 to gain 15%.

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