Important Concepts of Averages-Mixtures-Alligations for SSC CGL 2014 with Solved MCQs

Discussion in 'SSC' started by Lokesh Dhamija, Feb 25, 2014.

  1. Lokesh Dhamija

    Lokesh Dhamija Moderator Staff Member

    Study Material (Important Concepts) on Averages-Mixtures-Alligations for Staff Selection Commission Combined Graduate Level Exam 2014 (SSC CGL 2014) with solved MCQs(Mock/Sample Questions Solved)


    Averages:

    1. Averages of a group is defined as the ratio of sum of all the items in the group to the number of items in the group.


    Average = (Sum of all items in the group)/ Number of items in the group


    Now, sum of all items can be ‘the sum of number of quantities like apple, people etc’ or ‘sum of values of the item like 10 coins of 2Rs each etc’.


    Some Important Concepts:

    2. If the value of each item is increase by the same value a, then the average of the group or items will also increase by p.

    3. If the value of each item is decreased by the same value a, then the aveage of the group of items will also decrease by a.

    4. If the value of each item is multiplied by the same value a, then the average of the group or items will also get multiplied by a.

    5. If the value of each item is multiplied by the same value a, then the average of the group or items will also get divided by a.

    6. If we know only the average of the two groups individually, we cannot find out the average of the combined group of items.



    Weighted Averages:

    1. In weighted averages, items are multiplied by their quantities to find the total.

    Example: To find the average height of the students in the class, it will be calculated as follows:

    =(Total height of the entire class)/(total number of students in the entire class)


    Mixtures:

    1. Mixing of two or more quantities of things produces a mixture.

    2. When two mixtures of two qualities are mixed, then the quality of the resultant mixture is in between the quality of the two mixtures.

    3. Average quality is essentially the weighted average of the two constituent items.



    Examples 1: In an examination consisting of eight subjects, Ankit scored 85, 85, 90, 91, 92, 94, 95 and 96 marks. Find the average score scored by Ankit.

    Solution: The average score scored by Ankit will be

    = Sum of the scores / Number of subjects

    = (85 + 85 + 90 + 91 + 92 + 94 + 95 + 96) / 8

    = 728/8 = 91 marks


    Example 2: The average age of a group of 10 friends is 15 years. A new friend joins them and their average age increases to 16 years. What is the age of the new friend ?

    Solution: Average = (Sum of the items) / (Number of items)

    Sum of the items = (Number of items ) * (Average)

    Total Age of 10 friends = 10*15 = 150 years

    Total age of 11 friends after a new friend joins = 11*16 = 176 years

    Age of the new friend = 176 – 150 =26 years


    Example 3: The rainfall recorded by a city during the seven days of a week was as follows: 5cm per day on the first 3 days, 8cm on the fourth day, 10 cm on the fifth day, 12 cm on the sixth day and 7 cm on the seventh day. Find the average rainfall recorded per day during the week.

    Solution: Average rainfall = [(5*3) + 8+10 +12 +7] /7

    = 52/7 =7.4 cm


    Alligations:

    1. It is applied only in the case of weighed average.

    2. It is given as :

    q1/q2 =(p-p2) /(p1-p)


    where, q1= Is the quantity 1

    q2 = Is the quantity 2

    p1= Is the weight age of quantity 1

    p2 = Is the weight age of quantity 2


    Note: Free Questions with Solutions will be uploaded soon.

    You can also check our free material with Mock Questions (MCQs with Answers) on other quant topic from here: Click Here

    Feel Free to ask any doubt in any concept/question. Post your doubt directly below this post or create a new post/thread in the SSC Forum here: Click Here
  2. Divya111

    Divya111 New Member

    Hello,
    Thanks for Providing the Questions here for SSC CGL.
    It is really helpful for Exam Preparation.
    Click here to learn short Tricks of SSC CGL Reasoning here - Tricks to solve Number Series
    :)

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