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16 Nov 2020, 07:53
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No, it would just be good luck if that was true. In your solution, really all you're doing is guessing there are 30 students in one class, and 40 in the other. When you then discover that you do not have the 1 to 1 ratio the question tells you that you must have when you combine the classes, all you've proven is that it's impossible that there are 30 students in one class and 40 in the other. The numbers you've chosen don't agree with the information in the question, so it's impossible for them to be the correct numbers.
It would be perfectly fine here (not the best method, but it would be correct) to assume you have 10 boys and 20 girls in the first class. But once you choose numbers for one class, every other number will be determined by the ratios in the problem - you can't make up any other numbers. You could then solve by saying "we have g girls in the second class, and 3g boys, because of the 3 to 1 ratio", and you'd then have 10+3g boys and 20+g girls in the two classes combined. If these are in a 1 to 1 ratio, they're equal, so 10 + 3g = 20 + g, and g = 5. So in the second class we have 5 girls and 15 boys, and 20 students in total. The first class has 30 students in total. These are in a 3 to 2 ratio or 2 to 3 ratio, depending which number goes first (the question doesn't make that clear, but it needs to, so it's badly worded).
I'd prefer to just solve using alligation, but I won't go over that since you've said you know how to solve using that method.
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