An article when sold for ₦230.00 makes a 15% profit. Find the profit or loss % if it was sold for ₦180.00

1. Analyze the Question

We are given the selling price of an item and the profit percentage made at that price. We need to determine the profit or loss percentage if the selling price is reduced to a new value.

2. Explain the Concept

• Cost Price (CP): The original amount the item was bought for.
• Selling Price (SP): The amount the item is sold for.
• Profit % Formula: $\text{Profit \%} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100$
• Relationship: If an item is sold at a 15% profit, the Selling Price is $115\%$ of the Cost Price ($100\% + 15\%$).

3. Show the Solution

Step 1: Find the Cost Price (CP) We know that $115\%$ of the Cost Price = ₦230.00. Let $CP = x$. $1.15 \times x = 230$ $x = \frac{230}{1.15}$ $x = 200$ So, the Cost Price of the article is ₦200.00.

Step 2: Calculate the result for the new Selling Price The new Selling Price is ₦180.00. Since the new Selling Price (₦180) is less than the Cost Price (₦200), we have a loss.

Step 3: Calculate the loss percentage $\text{Loss} = \text{CP} - \text{New SP}$ $\text{Loss} = 200 - 180 = 20$

$\text{Loss \%} = \frac{\text{Loss}}{\text{CP}} \times 100$ $\text{Loss \%} = \frac{20}{200} \times 100$ $\text{Loss \%} = 0.1 \times 100 = 10\%$

4. Identify the Answer

The calculation shows a 10% loss. This matches option B.

5. Tip

When calculating profit or loss, always find the Cost Price first. It is the "anchor" for all your calculations. If your new Selling Price is lower than your Cost Price, you are guaranteed to have a loss; if it is higher, you have a gain.