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The first glass of lemonade had 200ml of lemon juice and 300ml of water. We could say that for every 200ml of lemon juice, there is 300ml of water. The ratio is 200:300.
If we simplify it, this means that for every 2ml of lemon, there is 3ml of water. We have divided both values by 100. Therefore we could express this as a ratio of 2:3.
The second glass of lemonade had 100ml of lemon juice and 200ml of water. We could say that for every 100ml of lemon juice, there is 200ml of water. The ratio is 100:200.
If we simplify it, this means that for every 1ml of lemon, there is 2ml of water. We have divided both values by 100. Therefore we could express this as a ratio of 1:2.
Now we have to make it so the second values are the same in order to compare them. I chose to make them both 6, as this is the LCM or lowest common multiple.
For the first one, we have multiplied the second number by 2 to get 6, so we multiply the first one by 2 as well. The new ratio is 4:6.
For the second one, we have multiplied the second number by 3 to get 6, so we multiply the first one by 3 also. The new ratio is 3:6.
Now we can compare them.
4:6 is larger than 3:6, so the first glass was stronger!
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If you wanted to do it in fractions/decimals/percentages then you could look at the diagram and realise that:
The first one has 2/5 lemon and 3/5 water. The second glass has 1/3 lemon and 2/3 water. If we convert to decimals then the first one would be 0.4 lemon and 0.6 water. The second one would be 0.33 lemon and 0.67 water. Therefore the first glass is stronger because it both add up to one, but the first one has more lemon and less water than the second.
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After a while of looking at this problem, I realised that there was a shorter but slightly more complex way. I realised that the difference between both glasses' water and juice was 100ml: each one had 100ml more water than juice. As a proportion, the extra 100ml would matter less in a larger glass, so therefore the larger (first) glass was stronger.
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Overall result: the first glass is stronger!