Question

A new spending tax of 25 percent is imposed on all electrical goods. A shop decides to reduce all of its electrical goods in a sale. What percentage reduction is needed to restore all prices to their pre-tax values? Consider an item that costs £100 before the tax is imposed.

a. 20%

b. 25%

c. 33.33%

d. 40%

Answer 1

A 20% reduction is needed to restore the prices of electrical goods to their pre-tax values after a 25% tax increase, returning the cost from £125 back to £100.

Step-by-step explanation:

To determine the percentage reduction needed to restore the prices of electrical goods to their pre-tax values after the imposition of a new spending tax, we can use a simple calculation. If an item originally costs £100, and a 25% tax is added, the new price becomes £100 + (£100 × 0.25) = £100 + £25 = £125. To reverse this increase, we want to find a percentage reduction that takes £125 back down to the original £100.

We use the formula for percentage decrease, which is (Original Price - New Price) / Original Price × 100%. Substituting the pre-tax price as the new price and the post-tax price as the original price, we have (£125 - £100) / £125 × 100% = £25 / £125 × 100%, which simplifies to 20%. Hence, a 20% reduction in the increased price would restore the electrical goods to their pre-tax prices.