If i gain 12% by selling an item for ₹1,232, then what would be my gain or loss percentage if I sell it for ₹1144?

Options

A. 6% gain
B. 6% loss
C. 4% gain
D. 4% loss

Answer

To solve the problem step by step, we need to find the cost price of the item first and then determine the gain or loss percentage when selling at a different price.

### Step 1: Calculate the Cost Price (CP)
Given that the selling price (SP) when a gain of 12% is made is ₹1,232, we can use the formula for selling price:

\[ SP = CP + \text{Gain} \]

Since Gain is 12% of the Cost Price (CP), we can express this as:

\[ \text{Gain} = \frac{12}{100} \times CP \]

Thus, we can rewrite the selling price equation as:

\[ SP = CP + \frac{12}{100} \times CP \]

This simplifies to:

\[ SP = CP \left(1 + \frac{12}{100}\right) = CP \left(\frac{112}{100}\right) \]

Now substituting the selling price:

\[ 1232 = CP \left(\frac{112}{100}\right) \]

To find CP, we rearrange the equation:

\[ CP = \frac{1232 \times 100}{112} \]

Calculating this gives:

\[ CP = \frac{123200}{112} = 1100 \]

### Step 2: Determine the new Selling Price (SP)
Now, we have a new selling price of ₹1,144.

### Step 3: Calculate Gain or Loss
To find out whether there is a gain or loss, we subtract the cost price from the new selling price:

\[ \text{Gain or Loss} = SP - CP = 1144 - 1100 = 44 \]

Since the selling price is greater than the cost price, this is a gain of ₹44.

### Step 4: Calculate Gain Percentage
Now, we calculate the gain percentage using the formula:

\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{CP}\right) \times 100 \]

Substituting the values we have:

\[ \text{Gain Percentage} = \left(\frac{44}{1100}\right) \times 100 \]

Calculating this gives:

\[ \text{Gain Percentage} = \frac{4400}{1100} = 4\% \]

### Final Answer
The gain percentage when selling the item for ₹1,144 is **4%**.

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