A company instead of raising the mark price by 20%, discounted the cost price by 20% while stitching the price tag on its product. Further the company offers a discount of 6.25% to its costomer. In this process company incurs a loss of Rs 37.5 on a single article. What was the cost price of that article.

Answer

To find the cost price of the article, we will follow these steps:

### Step 1: Understand the given information
- The company discounted the cost price by 20% instead of raising the mark price by 20%.
- A further discount of 6.25% was given to customers.
- The company incurred a loss of Rs 37.5 on a single article.

### Step 2: Let the cost price (CP) of the article be \( x \).
- The company discounted the cost price by 20%, so the selling price (SP) after the first discount is:
\[ SP = CP - (20\% \text{ of } CP) = x - 0.2x = 0.8x \]

### Step 3: Calculate the selling price after the second discount of 6.25%.
- The selling price after the second discount is:
\[ SP = 0.8x - (6.25\% \text{ of } 0.8x) = 0.8x - 0.0625 \times 0.8x = 0.8x \times (1 - 0.0625) = 0.8x \times 0.9375 \]
- Simplifying this gives:
\[ SP = 0.8 \times 0.9375x = 0.75x \]

### Step 4: Set up the equation for loss.
- The loss incurred is given as Rs 37.5. The loss can be calculated as:
\[ Loss = CP - SP \]
- Substituting the values gives:
\[ 37.5 = x - 0.75x \]
- This simplifies to:
\[ 37.5 = 0.25x \]

### Step 5: Solve for the cost price (CP).
- To find \( x \), we rearrange the equation:
\[ x = \frac{37.5}{0.25} = 150 \]

### Conclusion
- The cost price of the article is Rs 150.