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I have a basic school academic question which despite of trying very hard I was unable to find a solution -

Average score of girls is an exam is $67$ and that of boys is $62$. Find the percentage of girls and boys?

I think the question is incomplete - cause average is nothing but addition of each student marks divided by total number of student - and I was never able to find the solution - is my understanding correct - does an answer exists?

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Your understanding is correct. You need another piece of information - the overall average with boys and girls taken together. You can see that by constructing some examples.

If 80% of the students are girls then the overall average will be 66: 80% of the way from 62 to 67. If 80% are boys it will be 63.

You should be able to see how to work backwards from the overall average to the percentage of boys.

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You are right. The question is incomplete. Some more information is needed to solve the question.

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