Double Ratio Sharing for Paper 1 Non Calculator | Crossover GCSE Maths 14th May 2026 | REVISE9

追加: 2026-05-10

[00:00:00]So, in this question, we are looking at sharing in a ratio. We have a couple of different ways that we're going to be sharing in a ratio in this question.

[00:00:08]It says Chris, Debbie, and Errol share some money in the ratio 3:4:2.

[00:00:12]Debbie gets £120.

[00:00:16]Chris then gives some of his share to Debbie and some of his share to Errol.

[00:00:20]The money that Chris, Debbie, and Errol each have now is in the ratio 2:5:3.

[00:00:26]How much money did Chris give to Errol?

[00:00:29]Now, with a question like this where a ratio is changing, we might be tempted to look at these numbers and try and spot what's changed.

[00:00:39]But, really what we want to do is find the actual amount, the actual amount of money that's related to one of these ratios.

[00:00:48]Now, in this question, we've only been given this bit of information that Debbie gets £100.

[00:00:53]So, if we look at this first ratio, which is Chris, Debbie, and Errol, which is in the ratio 3:4:2, well, Debbie is underneath the four.

[00:01:07]As we are told Debbie gets £120, all we need to figure out is how did we get there?

[00:01:13]So, to get from four to 12, well, let's think from four to 12, which would be timesing by three, so this is timesing by 30.

[00:01:22]So, what we need to do is times them both by 30. So, 3 * 30 becomes 90, and 2 * 30 becomes 60.

[00:01:31]What we now have is all three parts in that original part of the story, and we can figure out how much they had in total.

[00:01:40]So, if we add all of these together, now again, I'm just going to use the nine, the 12, the starting numbers, the six. 9 add 12 is 21. Add six is 27. So, in total, there's £270 there.

[00:01:56]Now, that's what's being shared between these three people.

[00:02:00]But it says after some money was given away, so Chris gave some money to Debbie and some to Errol, now the ratio is 2 5 3.

[00:02:09]So Chris, Debbie, and Errol [clears throat] is now 2 5 and 3.

[00:02:17]But we now know the total.

[00:02:20]We know that that has to add up to £270.

[00:02:23]All they've done is swap the money around.

[00:02:26]>> [clears throat] >> So this ratio adds up to 10. There are 10 parts in this ratio, and we know there's £270.

[00:02:35]So we need to do £270 divided by the 10 parts, which is 27.

[00:02:41]And now we're going to need to multiply all of these by 27.

[00:02:46]Not the nicest of numbers to multiply by. 2 * 27 is 54.

[00:02:54]5 * 27, I probably want to take my time with that. 10 * 27 is 270. 5 * 27 is half of that. That might help you, it might not, but that's 135.

[00:03:05]So 135, if not, column multiplication to the side.

[00:03:12]3 * 27 is 27 more than 54. So if I add 7 to 54, that's 61. Add the 20, 81. So 81.

[00:03:23]So that is the new amount. And again, that still adds up to 270. No money's been given away, they've just swapped it between them.

[00:03:33]So what we want to know is how much money did Chris give to Errol?

[00:03:38]There's two ways of doing that. We could have a look at how much Chris's number has gone down by, or we could have a look at how much Errol's number has gone up by.

[00:03:52]Now, we need to read the question very carefully because it says Chris gives some of his share to Debbie and some of his share to Errol.

[00:04:02]So, if we look at how much Chris has gone down by, well, that's how much he gave away to Debbie and to Errol.

[00:04:10]So, really here, we just want to have a look at Errol's number.

[00:04:15]So, in order to figure that out, we do 81, how much Errol has now, take away the amount that Errol had at the start, and that is 21 pounds.

[00:04:28]And that's our final answer there, 21 pounds.

[00:04:32]Now, if we look, we can also see, not that it's asking this, Debbie's share has gone up by 15 pounds, which in total is 36. And if you look, Chris's share went from 90 down to 54, which is a loss of 36 pounds there. So, in total, those two differences add up to 36, which matches what Chris went down by. So, we know we've done it all correctly, and that is sharing in a ratio.

[00:04:56]Looking at it in two different ways, sharing when it's all three parts, which was the second process there, dividing by 10, and sharing when any one part is given.

[00:05:07]In the first part, where we were told Debbie gets 120.

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