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Two sections with one average k% more than the other and a combined average: find a section's average

This type of question, asked 3 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II. All 3 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    22
    The average score in Mathematics of 90 students of section A and B of class IX was 63. The number of students in A were 10 more than those in B. The average score of students in A was 30% more than that of students in B. The average score of students in B is:

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  2. Question 2

    29 Jan 2022 Tier II

    25
    The numbers of students in section A and section B of a class are 50 and 62, respectively. The average score in mathematics of all the students is 75. If the average score of students in section A is 20% more than that of students in section B, then what is the average score of students in section A (correct to one decimal place)?

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  3. Question 3

    3 Feb 2022 Tier II

    40
    The number of students in a class is 45, out of which 3313%33\frac{1}{3}\% are boys and the rest are girls. The average score of girls in Science is 6623%66\frac{2}{3}\% more than that of boys. If the average score of all the students is 78, then the average score of girls is:

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