A person incurs `5%` loss by selling a watch for Rs. 1140. At what price should the watch be sold to earn `5%` profit ?

Answer

To solve the problem step by step, we will follow the process of calculating the cost price (CP) first and then determining the selling price (SP) needed to achieve a 5% profit.

### Step 1: Identify the given values
- Selling Price (SP) when there is a loss = Rs. 1140
- Loss Percentage = 5%

### Step 2: Calculate the Cost Price (CP)
To find the cost price when there is a loss, we use the formula:
\[ CP = \frac{100}{100 - \text{Loss Percentage}} \times SP \]
Substituting the values:
\[ CP = \frac{100}{100 - 5} \times 1140 \]
\[ CP = \frac{100}{95} \times 1140 \]

### Step 3: Simplify the calculation
Now, let's simplify:
\[ CP = \frac{100 \times 1140}{95} \]
\[ CP = \frac{114000}{95} \]
Now, we can divide 114000 by 95:
\[ CP = 1200 \]

### Step 4: Calculate the Selling Price for 5% Profit
Now that we have the cost price, we can find the selling price for a 5% profit using the formula:
\[ SP = \frac{100 + \text{Profit Percentage}}{100} \times CP \]
Substituting the values:
\[ SP = \frac{100 + 5}{100} \times 1200 \]
\[ SP = \frac{105}{100} \times 1200 \]

### Step 5: Simplify the calculation
Now, let's simplify:
\[ SP = 1.05 \times 1200 \]
\[ SP = 1260 \]

### Conclusion
Thus, the selling price at which the watch should be sold to earn a 5% profit is **Rs. 1260**.

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