Smartphones are on sale. A smartphone now costs only 80% of its original price. By how many per cent would we need to increase the current price of the smartphone in order to bring it back to the original price?

Let a be the original price, b - the current price, and x - the answer we are looking for, so we need to increase b by x% in order to get a. So a=b+bx% (the original price a equals the current price b + the increase). We now need to solve for x. We are given that the current price b is 80% of the original price a, i.e. b=a80% This allows us to replace b with a80% in the equation above: a=a80%+a80%x% We can now divide both sides of the equations by a: 1=80%+80%x% 100%-80%=80%x% 20%=80%x% x%=20%/80%=20/80=1/4100%=25% So the answer is 25% Just in case, let's check our answer with real numbers. Suppose, the phone used to cost £500. Now it costs 80% of the original price, so 80%* £500= £400. In order to get back from £400 to £500 we need to increase the current price by 500-400= £100, which is 100/400=1/4=25% of the current price.