When an article is sold for Rupees 640, there is a loss of 12%. To gain 21%, it should be sold for:

Options

A. `774.40`
B. `880.00`
C. `770.00`
D. `828.80`

Answer

To find the selling price of an article when there is a gain of 21%, given that it was sold for Rs. 640 with a loss of 12%, we can follow these steps:

### Step 1: Determine the Cost Price (CP)
When an article is sold for Rs. 640 with a loss of 12%, we can use the formula for loss percentage:

\[ \text{Loss \%} = \frac{\text{CP} - \text{SP}}{\text{CP}} \times 100 \]

Here, Loss % = 12%, SP = 640.

Substituting the values, we have:

\[ 12 = \frac{\text{CP} - 640}{\text{CP}} \times 100 \]

### Step 2: Rearranging the Equation
To simplify, we can rearrange the equation:

\[ \frac{\text{CP} - 640}{\text{CP}} = \frac{12}{100} \]

Multiplying both sides by CP:

\[ \text{CP} - 640 = \frac{12 \cdot \text{CP}}{100} \]

### Step 3: Isolate CP
Now, we can isolate CP:

\[ \text{CP} - \frac{12 \cdot \text{CP}}{100} = 640 \]

This can be rewritten as:

\[ \text{CP} \left(1 - \frac{12}{100}\right) = 640 \]

Calculating \(1 - \frac{12}{100} = \frac{88}{100}\):

\[ \frac{88 \cdot \text{CP}}{100} = 640 \]

### Step 4: Solve for CP
Now, multiply both sides by \( \frac{100}{88} \):

\[ \text{CP} = 640 \times \frac{100}{88} \]

Calculating this gives:

\[ \text{CP} = \frac{64000}{88} = 727.27 \text{ (approximately)} \]

### Step 5: Calculate the Selling Price for 21% Gain
Now, we need to find the selling price (SP) for a 21% gain. The formula for gain percentage is:

\[ \text{Gain \%} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \]

Setting Gain % = 21%, we have:

\[ 21 = \frac{\text{SP} - 727.27}{727.27} \times 100 \]

### Step 6: Rearranging the Gain Equation
Rearranging gives:

\[ \frac{\text{SP} - 727.27}{727.27} = \frac{21}{100} \]

Multiplying both sides by 727.27:

\[ \text{SP} - 727.27 = 727.27 \times \frac{21}{100} \]

Calculating \(727.27 \times \frac{21}{100} = 152.73\):

\[ \text{SP} - 727.27 = 152.73 \]

### Step 7: Solve for SP
Now, adding 727.27 to both sides:

\[ \text{SP} = 727.27 + 152.73 = 880 \]

### Final Answer
Thus, the selling price to gain 21% is Rs. 880.

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