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Overall mean and the means of some subgroups: find the mean (or value) of the rest

This type of question, asked 6 times: CDS 2 2016, CDS 1 2017, CDS 1 2018, CDS 1 2020, CDS 1 2021, CDS 2 2023. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    92
    In a class of 100 students, there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls ?

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  2. Question 2

    CDS 1 2017

    52
    The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are

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  3. Question 3

    CDS 1 2018

    53
    The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?

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  4. Question 4

    CDS 1 2018

    45
    The average of the ages of 15 students in a class is 19 years. When 5 new students are admitted to the class, the average age of the class becomes 18.5 years. What is the average age of the 5 newly admitted students?

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  5. Question 5

    CDS 1 2020

    34
    In a class room the ratio of number of girls to that of boys is 3:43 : 4. The average height of students in the class is 4.6 feet. If the average height of the boys in the class is 4.8 feet, then what is the average height of the girls in the class ?

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  6. Question 6

    CDS 1 2021

    27
    Let the average score of a class of boys and girls in an examination be pp. The ratio of boys and girls in the class is 3:13 : 1. If the average score of the boys is (p+1)(p + 1), then what is the average score of the girls?

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  7. Question 7

    CDS 2 2023

    85
    The mean of p, q, r, s and t is 280. If the mean of p, r and t is 240, what is the mean of q and s ?

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