By selling an item for Rs. 1,035 , there is a gain of 15 % .If the item is sold for Rs. 922.50 ,then what is the gain loss percentage ?

Options

A. Loss , 12 .5%
B. Gain , 12.5%
C. Gain ,2.5%
D. Loss , 2.5 %

Answer

To solve the problem step by step, we need to find the cost price (CP) of the item first and then determine the gain or loss percentage when the item is sold for Rs. 922.50.

### Step 1: Find the Cost Price (CP)
We know that selling the item for Rs. 1,035 results in a gain of 15%.

The formula for selling price (SP) with gain percentage is:
\[ SP = CP + \text{Gain} \]
Where:
\[ \text{Gain} = \left( \frac{\text{Gain Percentage}}{100} \times CP \right) \]

Given:
- SP = Rs. 1,035
- Gain Percentage = 15%

We can express the gain in terms of CP:
\[ \text{Gain} = \frac{15}{100} \times CP = 0.15 \times CP \]

Substituting this into the SP formula gives:
\[ 1,035 = CP + 0.15 \times CP \]
\[ 1,035 = 1.15 \times CP \]

Now, we can solve for CP:
\[ CP = \frac{1,035}{1.15} \]
Calculating this:
\[ CP = 900 \]

### Step 2: Calculate Gain or Loss when sold for Rs. 922.50
Now, we need to determine if there is a gain or loss when the item is sold for Rs. 922.50.

Given:
- New SP = Rs. 922.50
- CP = Rs. 900

Now, we calculate the difference:
\[ \text{Loss} = CP - SP \]
\[ \text{Loss} = 900 - 922.50 = -22.50 \]

Since the result is negative, it indicates a loss of Rs. 22.50.

### Step 3: Calculate the Loss Percentage
The formula for loss percentage is:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP} \right) \times 100 \]

Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{22.50}{900} \right) \times 100 \]
Calculating this:
\[ \text{Loss Percentage} = \left( 0.025 \right) \times 100 = 2.5\% \]

### Conclusion
The loss percentage when the item is sold for Rs. 922.50 is **2.5%**.

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