Final answer:
To calculate the maximum discount on a vase to avoid a loss, we first find the original price, which is 45% above the £18,000 auction price, yielding £25,100. We then determine the discount percentage that results in the auction price, which is approximately 28.29%. The closest listed option without exceeding this value is 30%.
Step-by-step explanation:
The student is asking about calculating the maximum discount an antique dealer can give on a vase without incurring a loss, given that the vase was originally priced 45% above the auction price of £18,000. To find this percentage, we need to determine the original price and then calculate what percentage reduction would bring the price down to the auction value. Since the original price is 45% above the auction price, we first calculate the increase: 45% of £18,000 equals £7,100 (£18,000 * 0.45). So the original price is £18,000 + £7,100 = £25,100. The maximum discount percentage is the discount at which the sale price would equal the auction price. If the dealer reduces the price by any percentage, it means they are selling it for that percentage less than £25,100. If the dealer reduces the price to the auction price of £18,000, the discount percentage would be (£25,100 - £18,000)/£25,100, which is £7,100/£25,100, or approximately 28.29%. Therefore, the closest option without going over the actual percentage is option B: 30%.