By selling a wrist watch at Rs. 405 the shopkeeper incurs a loss of 10%. What is the gain or loss percentage if he sells the same watch at Rs. 465 ?

Options

A. profit of 10%
B. loss of 6%
C. profit of 3.33%
D. no profit no loss

Answer

To solve the problem step by step, we will first determine the cost price of the wristwatch based on the information given about the selling price and the loss percentage. Then, we will calculate the gain or loss percentage when the watch is sold at a different price.

### Step 1: Calculate the Cost Price (CP)
We know that the selling price (SP) is Rs. 405 and the shopkeeper incurs a loss of 10%. This means that the selling price is 90% of the cost price.

Using the formula:
\[ SP = CP \times \left( \frac{100 - \text{Loss \%}}{100} \right) \]
Substituting the values:
\[ 405 = CP \times \left( \frac{100 - 10}{100} \right) \]
\[ 405 = CP \times 0.90 \]
To find the cost price (CP), we rearrange the equation:
\[ CP = \frac{405}{0.90} \]
Calculating this gives:
\[ CP = 450 \]

### Step 2: Determine the New Selling Price (SP)
The new selling price is given as Rs. 465.

### Step 3: Calculate the Profit or Loss
Now, we need to determine whether there is a profit or loss when the watch is sold at Rs. 465.

Profit or Loss can be calculated using the formula:
\[ \text{Profit or Loss} = SP - CP \]
Substituting the values:
\[ \text{Profit} = 465 - 450 = 15 \]

### Step 4: Calculate the Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit \%} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Profit \%} = \left( \frac{15}{450} \right) \times 100 \]
Calculating this gives:
\[ \text{Profit \%} = \left( \frac{15}{450} \right) \times 100 = \frac{1500}{450} = \frac{100}{30} \approx 3.33\% \]

### Final Answer
The gain percentage when the wristwatch is sold at Rs. 465 is approximately **3.33%**.

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