A high-end audio equipment retailer acquired a digital synthesizer for $1,500. The store set the retail tag price at 40% above the procurement cost, but later provided a 15% discount on this tag price during a promotional sale. What is the net percentage profit or loss realized on this transaction?

The correct option is 19% Profit.

To find the net percentage profit or loss realized on this transaction, we can analyze the step-by-step changes in price starting from the procurement cost.

Step 1: Calculate the retail tag price (Marked Price).

The procurement cost (Cost Price) of the digital synthesizer is $1,500. The retailer marks up the price by 40% above the procurement cost:

$\text{Marked Price}=\text{Cost Price}\times \left(1+\frac{40}{100}\right)$

$\text{Marked Price}=\$1500\times 1.40=\$2100$

Step 2: Calculate the promotional selling price.

During a promotional sale, a 15% discount is offered on the retail tag price:

$\text{Selling Price}=\text{Marked Price}\times \left(1-\frac{15}{100}\right)$

$\text{Selling Price}=\$2100\times 0.85=\$1785$

Step 3: Determine the profit amount.

Profit is calculated as the selling price minus the procurement cost:

$\text{Profit}=\text{Selling Price}-\text{Cost Price}$

$\text{Profit}=\$1785-\$1500=\$285$

Step 4: Calculate the net percentage profit.

The net percentage profit relative to the procurement cost is:

$\text{Net Percentage Profit}=\left(\frac{\text{Profit}}{\text{Cost Price}}\right)\times 100\%$

$\text{Net Percentage Profit}=\left(\frac{285}{1500}\right)\times 100\%=0.19\times 100\%=19\%$

Alternative Direct Percentage Method:

We can also compute the overall multiplier by combining the 40% markup and the 15% discount:

$\text{Net Multiplier}=1.40\times 0.85=1.19$

$\text{Net Profit \%}=\left(1.19-1\right)\times 100\%=19\%$

Since the resulting value is positive, the retailer realized a net profit of 19% on this transaction.