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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. 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. 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%.
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 1,800 pounds.
Because 1,800 pounds represents one percent, all we have to do to find the original price, which remember we said earlier was 100%, is multiply 1,800 pounds by 100. This shows us that the original price was 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 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 100%, we first need to find one percent by dividing the 207,000 by 115, which is 1,800 pounds. Then we can multiply that by 100 to show that the original price was 180,000 pounds.
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. Once you find out what one percent is worth, you can use that to find out the value of any percentage that you want.
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. We know that once it's been reduced by 20%, 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%, 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%.
This means that to find 1%, we just have to divide 72 pounds by 80 to get 0.9 pounds. 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 8% in the first year to 12,880 pounds. What was the original price of the car?
Well, this time, 12,880 pounds is a new price, and we know that it's decreased by 8% from the original price, which we don't know the exact value of but we can think of as 100%.
This means that the new price must be 100% minus 8% or 92% of the original. So, we're going to have to do 12,880 divided by 92 to find that 1% is 140 pounds.
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 has 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 5% 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 5% and that the actual value of that 5% increase is 42 pounds 50. So, this time, to find 1%, like we've been doing for the other questions, we need to divide the 42 pounds 50 by 5 to find that 1% is 8 pounds 50.
Now, to work out the original price, we can just multiply the 8 pounds 50 by 100 to get 850 pounds. So, the seasonal tickets cost 850 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% plus the extra 5%, which gives us 105%.
So, that will be 892 pounds 50. 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 8 pounds 10. What was the original price of the dress?
So, this time, the 8 pounds 10 represents the 18% reduction from the original price of 100%. To find 1%, we need to divide 8 pounds 10 by 18, which is 0.45 pounds.
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.
I definitely recommend just doing a whole bunch of exam questions and checking the mark scheme 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.