How can I solve reverse percentage questions?

A bag in a sale is reduced by 20%. It now costs £40. What was the original price? Solution 1: Using ratios and basic percentagesA good way to solve this problem is by thinking about what percentage is left after the bag has been reduced. In the question above the bag has been reduced by 20%, so 80% of the original price is left. The question tells you that after the reduction the cost is £40. This means that 80% = £40. We are trying to find the original price which is 100%. 80% = £4010% = £5100% = £50Therefore the original price is £50. Make sure to always check your answer makes sense. Because we are finding the price of the bag before it was reduced our answer must be bigger than £40, the sale price. Solution 2: Using multipliersTo reduce something by 20% you multiply it by 0.8. This means that:Original price x 0.8 = £40You can work backwards to find the original price, by dividing £40 by 0.8.£40/0.8 = £50Extension:Instead of using 'Original price' in solution 2, you can use x. This gives:0.8x = 40Solving the equation gives x = 50Though this may seem very similar to the second solution, using algebra can help in more complex problems where there are two or more steps to the reduction. Q. The price of the bag is halved and then reduced by £5 to give a new price of £20 0.5x -5 = 200.5x = 25x = 50