Question

An antique dealer tries to sell a vase at 45% above the £18000 which the dealer paid at auction. By which percentage can the dealer reduce the price before making a loss?

a) 31%
b) 39%
c) 35%
d) 21%
e) 27%
f) 29%

Answer 1

The dealer can reduce the price by 29% before making a loss on the vase.

Step-by-step explanation:

To find the percentage by which the dealer can reduce the price before making a loss, we need to consider the profit percentage and the cost price. The dealer tries to sell the vase at 45% above the £18000 cost price. So, the selling price would be £18000 + 45% of £18000. This can be calculated as £18000 + (45/100) * £18000.

Now, to find the percentage by which the dealer can reduce the price before making a loss, we need to calculate the selling price for different percentage reductions. Let's consider a reduction of x%. In that case, the selling price would be (£18000 + (45/100) * £18000) - x% of (£18000 + (45/100) * £18000).

If the selling price is equal to the cost price, then the dealer would break even. So, we can set up the equation (£18000 + (45/100) * £18000) - x% of (£18000 + (45/100) * £18000) = £18000.

Simplifying the equation, we can solve for x to find the percentage by which the dealer can reduce the price before making a loss.

Therefore, the dealer can reduce the price by 29% before making a loss on the vase.