[Music] in today's video we're going to look at how we can find the original value of something after it's already changed by a certain percentage and we sometimes call this reverse percentages for example let's take this question where we're told that the price of a house has increased by 15 and now costs 207 000 pounds and we're being asked to find out what the original price must have been so in this scenario the 207 000 pounds is the new price after some original price which we don't know yet has been increased by 15 the best way to think about these questions is to remember that the original price is always equivalent to 100 so in this example where the price has increased by 15 the new price is effectively 115 because we can think of it as the original 100 plus the extra 15 which is 115 in total this way of doing it is actually really helpful because it means that we can find out what one percent is by dividing the 207 000 pounds by 115 to get 1800 pounds and because thousand eight hundred pounds represents one percent all we have to do to find the original price which remember we said earlier was a hundred percent is multiply one thousand eight hundred pounds by a hundred showing us that the original price was a 180 000 pounds now this here is a little bit messy and potentially a bit confusing so you don't really want to allow your workings like this in the exam instead you want to first of all think of the 207 000 pounds as equivalent to 115 of the original value so if we want to find the original value which is a hundred percent we first need to find one percent by dividing the 207 000 by 115 which is 1800 pounds and then we can multiply that by 100 to show that the original price was 180 000 pounds so basically this technique and in fact every example that we're going to look at in this video is all about finding out the value of one percent and once you find out what one percent is worth you can use that to find out the value of any percentage that you want and this way of doing it in the box here is basically the simplest way of showing your workings and this is how i would write this question in the exams let's try doing this for another one in a christmas sale all the prices have been reduced by 20 if zara buys a pair of sunglasses for 72 pounds what was the original price of the sunglasses so in this question we're looking for the original price before it was discounted and we know that once it's been reduced by 20 percent the new price is 72 pounds just like before we can think of the original price as 100 so if it's been reduced by 20 percent then the new sale price must be 80 because 100 minus 20 is 80. so we now know that 72 pounds is equivalent to 80 and this means that to find 1 we just have to divide 72 pounds by 80 to get 0.9 pounds and then to find the original price we just multiply this 0.9 by 100 to get 90 pounds so the sunglasses must have cost 90 pounds before the sale okay so for this one it says that the value of a car decreased by eight percent in the first year to twelve thousand eight hundred and eighty pounds what was the original price of the car well this time twelve thousand eight hundred eighty pounds is a new price and we know that it's decreased by eight percent from the original price which we don't know the exact value of but we can think of as a hundred percent this means that the new price must be 100 minus eight or 92 percent of the original so we're going to have to do 12 880 divided by 92 to find that 1 is 140 pounds and then we can multiply that by 100 to find that the original price must have been 14 000 pounds now just before we finish we need to look at a slightly different version of these reverse percentage questions which are ones where they tell you how much the price is changed by rather than telling you the new price for example in this question here we're told that the price of all seasonal rail tickets increased by five percent and that the price of the london to bristol ticket increased by 42 pounds 50. what did the ticket cost before and after the increase so just like before let's think of it in terms of the original price which is 100 and a new price but this time it's a bit different because we don't know the value of the new price instead we're given extra details about the change in price the question tells us that the price has increased by five percent and that the actual value of that five percent increase is 42 pounds 50. so this time to find one percent like we've been doing for the other questions we need to divide the 42 pounds 50 by five to find that one percent is eight pounds fifty and so now to work out the original price we can just multiply the eight pounds fifty by one hundred to get eight hundred and fifty pounds so the seasonal tickets cost eight hundred and fifty pounds before the price increase then to find the new price after the increase we just multiply 8 pounds 50 by 105 because we want the original 100 percent plus the extra 5 which gives us 105 so that will be 892 pounds 50. or alternatively you could have also just added the original price of 850 pounds to the change in price of 42.50 and that would have also given you 892.50 so either way of doing it is perfectly fine let's try one more of this type during an 18 summer sale the price of a dress was reduced by eight pounds ten what was the original price of the dress so this time the eight pounds ten represents the eighteen percent reduction from the original price of a hundred percent so to find one percent we need to divide eight pounds ten by eighteen which is zero point four five pounds and then to find the original price we just multiply this by 100 to get 45 pounds so the original price was 45 pounds anyway that's the end of this video so i hope that all made sense don't worry if you find this technique quite tricky it does take a bit of getting used to and i definitely recommend it just doing a whole bunch of exam questions and just check the mark seem after every single one but anyway if you found it useful then please give us a like and subscribe and we'll see you again soon you