Question

The selling price of 30 items is equal to the purchase price of 25 items, then the profit or loss percent is:

• A. \( 16\frac{2}{3}% \)
• B. \( 18\frac{2}{3}% \)
• C. \( 14\frac{2}{3}% \)
• D. \( 15\frac{2}{3}% \)

Hint:

To find the profit or loss percentage, relate \( SP \) and \( CP \). If \( SP>CP \), there's a profit; if \( SP<CP \), there's a loss.

Answer 1

The Correct Option is A

Step 1: Define the variables and the given information.
Let the selling price of one item be \( SP \). Let the purchase price (or cost price) of one item be \( CP \). We are given that the selling price of 30 items is equal to the purchase price of 25 items: \[ 30 \times SP = 25 \times CP \] Step 2: Establish a relationship between the selling price and the purchase price.
From the given condition, \( 30 \times SP = 25 \times CP \), we can find the ratio of \( SP \) to \( CP \): \[ \frac{SP}{CP} = \frac{25}{30} = \frac{5}{6} \] This implies \( SP = \frac{5}{6} CP \). Step 3: Determine if there is a profit or loss.
Since \( SP<CP \), there is a loss. Step 4: Calculate the loss.
Loss = \( CP - SP = CP - \frac{5}{6} CP = \frac{1}{6} CP \) Step 5: Calculate the loss percentage.
Loss % = \( \frac{Loss}{CP} \times 100 = \frac{\frac{1}{6} CP}{CP} \times 100 = \frac{1}{6} \times 100 = \frac{100}{6} % = \frac{50}{3} % \) Step 6: Express the loss percentage as a mixed fraction. \[ \frac{50}{3} % = 16 \frac{2}{3}% \]