By selling an article for ₹820, Abhi looses 18%. To gain 25.5%, he should sell it for:

Options

A. ₹1,260
B. ₹1,275
C. ₹1,255
D. ₹1,250

Answer

To solve the problem step by step, we need to find the cost price of the article first and then calculate the selling price required to achieve a gain of 25.5%.

### Step 1: Identify the Selling Price and Loss Percentage
- Given Selling Price (SP) = ₹820
- Loss Percentage = 18%

### Step 2: Calculate the Cost Price (CP)
The formula to find the cost price when the selling price and loss percentage are known is:
\[ CP = \frac{SP \times 100}{100 - \text{Loss Percentage}} \]
Substituting the values:
\[ CP = \frac{820 \times 100}{100 - 18} \]
\[ CP = \frac{820 \times 100}{82} \]

### Step 3: Perform the Calculation
Calculating the above expression:
\[ CP = \frac{82000}{82} \]
\[ CP = 1000 \]
So, the Cost Price (CP) is ₹1000.

### Step 4: Calculate the Selling Price for Desired Gain
Now, we need to find the selling price that gives a gain of 25.5%. The formula for selling price when the cost price and gain percentage are known is:
\[ SP = CP \times \left(1 + \frac{\text{Gain Percentage}}{100}\right) \]
Substituting the values:
\[ SP = 1000 \times \left(1 + \frac{25.5}{100}\right) \]
\[ SP = 1000 \times \left(1 + 0.255\right) \]
\[ SP = 1000 \times 1.255 \]

### Step 5: Perform the Calculation
Calculating the above expression:
\[ SP = 1255 \]

### Conclusion
To gain 25.5%, Abhi should sell the article for ₹1255.

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