Question

A furniture store has a sale of 40% off on selected items. A sales assistant, Carol, reduces the price of a sofa originally costing $1200. (a) What is the new price? The manager does not want this sofa to be in the sale and the following day tells another sales assistant, Michael, to restore the sofa back to the original price. He does not know what the original price was and decides to show off his mathematical knowledge by taking the answer to part (a) and multiplying it by 1.4. (b) Explain carefully why this does not give the correct answer of $1200. (c) Suggest an alternative calculation that would give the right answer

Answer 1

a) the new price will be (1 - 40%) of the original price, i.e., 60% of the original price, i.e., $1200 * 60% = $720

b) when Michael does 1.4 times of $720, he gets $1,008 which is not equal to the original price. The reason is that 60% * 1.4 equals only 0.84 and not 1, which we need to get back to

c) the right way to restore the original price is to divide the discounted price by (1 - rate of discount) in any similar situation. Here when we do this we get $720 / (1-40%) = $720/60% = $1200