When a shopkeeper sells item A for ₹ 384, then there is a loss of 20% and when he sells item B for ₹ 400, then there is a profit of 25%. What is the profit/loss percent, if he sells both items for a total of ₹ 852?

Question

Accepted Answer

To determine the profit or loss percentage when both items A and B are sold for a total of ₹ 852, we need to first calculate the cost price of each item.

1. **Item A:**
   - Selling Price (SP) of item A = ₹ 384
   - Loss = 20%
   - Let the Cost Price (CP) of item A be ₹ x.
   - Since there is a loss of 20%, SP = CP - 20% of CP
   - Therefore, 384 = x - 0.2x = 0.8x
   - Solving for x, we get x = 384 / 0.8 = ₹ 480

2. **Item B:**
   - Selling Price (SP) of item B = ₹ 400
   - Profit = 25%
   - Let the Cost Price (CP) of item B be ₹ y.
   - Since there is a profit of 25%, SP = CP + 25% of CP
   - Therefore, 400 = y + 0.25y = 1.25y
   - Solving for y, we get y = 400 / 1.25 = ₹ 320

3. **Total Cost Price and Selling Price:**
   - Total CP of both items = CP of A + CP of B = ₹ 480 + ₹ 320 = ₹ 800
   - Total SP of both items = ₹ 852

4. **Profit/Loss Calculation:**
   - Profit = Total SP - Total CP = ₹ 852 - ₹ 800 = ₹ 52
   - Profit Percentage = (Profit / Total CP) × 100 = (52 / 800) × 100 = 6.5%

Therefore, the profit percentage when both items are sold for a total of ₹ 852 is 6.5%, which corresponds to Option 1: Profit, 6.5%.

**Explanation of Incorrect Options:**

- **Option 2: Loss, 5%**
  - This option is incorrect because we calculated a profit, not a loss. The total selling price exceeds the total cost price, resulting in a profit, not a loss.

- **Option 3: Loss, 7%**
  - Similar to Option 2, this option is incorrect because there is no loss. The calculation clearly shows a profit of 6.5%, not a loss.

- **Option 4: Profit, 7.5%**
  - This option is incorrect because the calculated profit percentage is 6.5%, not 7.5%. The difference between the total selling price and total cost price results in a 6.5% profit.

In conclusion, the correct answer is Option 1: Profit, 6.5%, as the calculations clearly support this outcome.