By reducing the selling price of an article by Rs 50, a gain of 5% turns into a loss of 5%. Find the original selling price of the article.

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript and break it down into clear steps.

### Step 1: Understand the Problem
We know that reducing the selling price of an article by Rs. 50 changes a gain of 5% into a loss of 5%. We need to find the original selling price of the article.

### Step 2: Define Variables
Let:
- \( CP \) = Cost Price of the article
- \( SP \) = Original Selling Price of the article

### Step 3: Calculate the Selling Price with Gain
From the problem, when there is a gain of 5%, the selling price can be expressed as:
\[ SP = CP + 5\% \text{ of } CP \]
\[ SP = CP + \frac{5}{100} \times CP \]
\[ SP = CP \left(1 + \frac{5}{100}\right) \]
\[ SP = CP \left(\frac{105}{100}\right) \]
\[ SP = \frac{105}{100} \times CP \]

### Step 4: Calculate the Selling Price with Loss
When the selling price is reduced by Rs. 50, the new selling price becomes:
\[ SP - 50 \]
At this new selling price, there is a loss of 5%, which can be expressed as:
\[ SP - 50 = CP - 5\% \text{ of } CP \]
\[ SP - 50 = CP - \frac{5}{100} \times CP \]
\[ SP - 50 = CP \left(1 - \frac{5}{100}\right) \]
\[ SP - 50 = CP \left(\frac{95}{100}\right) \]
\[ SP - 50 = \frac{95}{100} \times CP \]

### Step 5: Set Up the Equation
Now we have two expressions for \( SP \):
1. \( SP = \frac{105}{100} \times CP \)
2. \( SP - 50 = \frac{95}{100} \times CP \)

We can substitute the first equation into the second:
\[ \frac{105}{100} \times CP - 50 = \frac{95}{100} \times CP \]

### Step 6: Solve for Cost Price (CP)
Rearranging the equation gives:
\[ \frac{105}{100} \times CP - \frac{95}{100} \times CP = 50 \]
\[ \left(\frac{105 - 95}{100}\right) \times CP = 50 \]
\[ \frac{10}{100} \times CP = 50 \]
\[ \frac{1}{10} \times CP = 50 \]
Multiplying both sides by 10:
\[ CP = 500 \]

### Step 7: Calculate the Original Selling Price (SP)
Now that we have \( CP \), we can find the original selling price:
\[ SP = \frac{105}{100} \times CP \]
\[ SP = \frac{105}{100} \times 500 \]
\[ SP = 525 \]

### Final Answer
The original selling price of the article is Rs. 525.

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