I gain `19%` if I sell an article for Rs. 595 .What would be my gain or loss percentage if I sell it for Rs. 475 ?

Options

A. Gain `5%`
B. Loss `5%`
C. Loss `10%`
D. Gain `10%`

Answer

To solve the problem step by step, we will follow the calculations as described in the video transcript.

### Step 1: Understand the Given Information
- Gain Percentage (GP) = 19%
- Selling Price (SP1) = Rs. 595

### Step 2: Calculate the Cost Price (CP)
Using the formula for Selling Price in terms of Cost Price and Gain Percentage:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Where Gain can be expressed as:
\[ \text{Gain} = \frac{\text{GP}}{100} \times \text{CP} \]

So we can rewrite the Selling Price as:
\[ \text{SP} = \text{CP} + \frac{19}{100} \times \text{CP} \]
\[ \text{SP} = \text{CP} \left(1 + \frac{19}{100}\right) \]
\[ \text{SP} = \text{CP} \times \frac{119}{100} \]

Now, substituting the given SP:
\[ 595 = \text{CP} \times \frac{119}{100} \]

To find CP, we rearrange the equation:
\[ \text{CP} = 595 \times \frac{100}{119} \]

Calculating CP:
\[ \text{CP} = 595 \times 0.84034 \approx 500 \]

### Step 3: Calculate Loss when Selling at Rs. 475
Now, we have:
- Cost Price (CP) = Rs. 500
- Selling Price (SP2) = Rs. 475

To find the loss:
\[ \text{Loss} = \text{CP} - \text{SP2} \]
\[ \text{Loss} = 500 - 475 = 25 \]

### Step 4: Calculate Loss Percentage
Using the formula for Loss Percentage:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left(\frac{25}{500}\right) \times 100 \]

Calculating Loss Percentage:
\[ \text{Loss Percentage} = 0.05 \times 100 = 5\% \]

### Final Answer
The loss percentage when selling the article for Rs. 475 is **5%**.

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