Question

A merchant earns \(25%\) profit in general. Once his \(25%\) consignment was abducted forever by some thieves. Trying to compensate for his loss he sold the rest of his consignment by increasing his selling price by \(20%\). What is the new percentage profit or loss?

• A. \(10%\) loss
• B. \(12.5%\) loss
• C. \(12.5%\) profit
• D. \(10%\) profit

Hint:

Even though $25%$ of his goods are gone, the "Total CP" is still based on the original 100 units because that is the amount he invested initially. Always use the original total investment as the base for net profit/loss.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The net profit or loss depends on the total Cost Price (CP) spent on the entire consignment compared to the total Selling Price (SP) realized from the remaining goods.
Step 2: Key Formula or Approach:
\[ \text{Profit/Loss %} = \frac{\text{Total SP} - \text{Total CP}}{\text{Total CP}} \times 100 \] Step 3: Detailed Explanation:
1. Let the total quantity of the consignment be \(100\) units and the Cost Price of each unit be \(₹ 1\).
Total CP = \(100 \times 1 = ₹ 100\).
2. The initial general profit is \(25%\). So, the general SP per unit = \(1 \times (1 + 0.25) = ₹ 1.25\).
3. A \(25%\) consignment was stolen. So, quantity stolen = \(25\) units. Remaining quantity = \(100 - 25 = 75\) units.
4. To compensate, he increases his selling price by \(20%\).
New SP per unit = \(1.25 \times (1 + 0.20) = 1.25 \times 1.2 = ₹ 1.50\).
5. Total SP realized from selling the remaining \(75\) units = \(75 \times 1.5 = ₹ 112.50\).
6. Net Profit = Total SP \(-\) Total CP = \(112.50 - 100 = ₹ 12.50\).
7. Profit % = \(\frac{12.5}{100} \times 100 = 12.5%\).
Step 4: Final Answer:
The merchant makes a net profit of \(12.5%\).