On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of

### Concept & Formula A discount percentage on "buy $x$, get $y$ free" offers is calculated based on the total number of items the customer walks away with, not just the items paid for. $$ \text{Discount \%} = \frac{\text{Free Items}}{\text{Total Items Received}} \times 100 $$ ### Step-by-Step Solution 1. The retailer orders and pays for 5 dozen boxes. 2. The retailer receives 1 dozen boxes for free. 3. Total number of boxes received = 5 dozen (paid) + 1 dozen (free) = 6 dozen. 4. The discount is essentially the cost of the 1 free dozen out of the total 6 dozen received. 5. Discount % = $(\frac{1}{6}) \times 100$. 6. Calculate the value: $\frac{100}{6} = \frac{50}{3} = 16 \frac{2}{3}\%$. ### Exam Strategy & Shortcut Do not convert dozens to individual units (60 and 12). Keep the ratio simple: 1 free out of 6 total. $1/6$ is a standard fraction equivalent to $16.66\%$ or $16 \frac{2}{3}\%$. Memorizing standard fraction-to-percentage conversions saves time. ### Common Pitfall The most common mistake is calculating the percentage over the paid items instead of the total items (i.e., $1/5 = 20\%$). The marked price total always applies to all items received. ### Final Answer Therefore, the correct answer is **$16 \frac{2}{3}\%$**.