A trader sold an item at a loss of 20%. Had he sold it for ₹100 more, he would have gained a profit of 5%. What is the cost price of the item ?

Options

A. ₹ 250
B. ₹ 200
C. ₹ 25
D. ₹ 400

Answer

To find the cost price of the item, let's denote the cost price as \( CP \).

1. **Understanding the Loss**:
The trader sold the item at a loss of 20%. This means he sold it for 80% of the cost price.
Therefore, the selling price (SP) when sold at a loss of 20% can be calculated as:
\[ SP = CP - (20\% \text{ of } CP) = CP - 0.2 \times CP = 0.8 \times CP \]

2. **Understanding the Profit**:
If he had sold it for ₹100 more, he would have gained a profit of 5%. This means the new selling price would be:
\[ SP + 100 = CP + (5\% \text{ of } CP) = CP + 0.05 \times CP = 1.05 \times CP \]

3. **Setting Up the Equation**:
From the above two points, we can set up the equation:
\[ 0.8 \times CP + 100 = 1.05 \times CP \]

4. **Solving the Equation**:
Rearranging the equation gives:
\[ 100 = 1.05 \times CP - 0.8 \times CP \]
\[ 100 = (1.05 - 0.8) \times CP \]
\[ 100 = 0.25 \times CP \]
\[ CP = \frac{100}{0.25} = 400 \]

5. **Conclusion**:
The cost price of the item is ₹400.