Average


  1. In a class, there are 40 boys and their average age is 16 years. One boy, aged 17 years, leaving the class and another joining, the average age becomes 15.875 years. The age of the new boy is :









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    Given that , Age of replaced boy = 17 years
    The average age of 40 boys = 16 years.
    Total age of 40 boys = 40 × 16 = 640 years
    New total age of 40 boys = 40 × 15.875 = 635 years
    ∴ Age of new boy = [635 – (640 – 17)] = 12 years
    Second method to solve this question with the help of given formula :
    Here, n = 40 , X = 16 – 15.875 ⇒ X = 0.125
    Age of new boy = Age of replaced boy – Xn

    Correct Option: A

    Given that , Age of replaced boy = 17 years
    The average age of 40 boys = 16 years.
    Total age of 40 boys = 40 × 16 = 640 years
    New total age of 40 boys = 40 × 15.875 = 635 years
    ∴ Age of new boy = [635 – (640 – 17)] = 12 years
    Second method to solve this question with the help of given formula :
    Here, n = 40 , X = 16 – 15.875 ⇒ X = 0.125
    Age of new boy = Age of replaced boy – Xn
    Age of new boy = 17 – 0.125 × 40 = 17 – 5
    Age of new boy = 12 years


  1. The average age of 12 players of a team is 25 years. If the captain’s age is included, the average age increases by 1 year. The age of the captain is :









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    The average age of 12 players of a team = 25 years.
    Total age of 12 players = 12 × 25 = 300
    Total age including captain = 13 × 26 = 338
    ∴ Age of the captain = 338 – 300 = 38 years
    Second method to solve this question with the help of given formula :
    Here, X = 1, n = 12

    Correct Option: B

    The average age of 12 players of a team = 25 years.
    Total age of 12 players = 12 × 25 = 300
    Total age including captain = 13 × 26 = 338
    ∴ Age of the captain = 338 – 300 = 38 years
    Second method to solve this question with the help of given formula :
    Here, X = 1, n = 12
    Age of the captain = Average + X (n + 1)
    Age of the captain = 25 + 1 (12 + 1) = 38 years



  1. The average age of A and B is 20 years. If A is to be replaced by C, the average would be 19 years. The average age of C and A is 21 years. The ages of A, B and C in order (in years) are









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    Given that , The average age of A and B = 20 years
    ⇒ A + B = 2 × 20 = 40 .....( 1 )
    If A is to be replaced by C, the average of C and B = 19 years
    ⇒ C + B = 2 × 19 = 38 .....( 2 )
    The average age of C and A = 21 years
    ⇒ C + A = 2 × 21 = 42 .....( 3 )
    On adding all three equations , 2 (A + B + C) = 40 + 38 + 42 = 120
    ⇒ A + B + C = 60
    ∴ A = (A + B + C) – (B + C) = 60 – 38 = 22 years

    Correct Option: C

    Given that , The average age of A and B = 20 years
    ⇒ A + B = 2 × 20 = 40 .....( 1 )
    If A is to be replaced by C, the average of C and B = 19 years
    ⇒ C + B = 2 × 19 = 38 .....( 2 )
    The average age of C and A = 21 years
    ⇒ C + A = 2 × 21 = 42 .....( 3 )
    On adding all three equations , 2 (A + B + C) = 40 + 38 + 42 = 120
    ⇒ A + B + C = 60
    ∴ A = (A + B + C) – (B + C) = 60 – 38 = 22 years
    B = (A + B + C) – (A + C) = 60 – 42 = 18 years
    ∴ C = (A + B + C) – (A + B) = 60 – 40 = 20 years


  1. The average age of Ram and his two children is 17 years and the average age of Ram’s wife and the same children is 16 years. If the age of Ram is 33 years, the age of his wife is (in years):









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    Here , Age of Ram = 33 years
    The average age of Ram and his two children = 17 years
    ⇒ Ram + two children = 51 years .... ( 1 )
    and the average age of Ram’s wife and the same children = 16 years.
    ⇒ His wife + two children = 48 years .... ( 2 )
    From eq. ( 1 ) - ( 2 ) , we get
    ∴ Ram – wife = 3 years

    Correct Option: D

    Here , Age of Ram = 33 years
    The average age of Ram and his two children = 17 years
    ⇒ Ram + two children = 51 years .... ( 1 )
    and the average age of Ram’s wife and the same children = 16 years.
    ⇒ His wife + two children = 48 years .... ( 2 )
    From eq. ( 1 ) - ( 2 ) , we get
    ∴ Ram – wife = 3 years
    ⇒ 33 – wife = 3 years
    ∴ Wife = 33 – 3 = 30 years



  1. From a class of 42 boys, a boy aged 10 years goes away and in his place, a new boy is admitted. If on account of this change, the average age of the boys in that class increases by 2 months, the age of the newcomer is :









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    According to question ,
    Total increase = 2 × 42

    Age of new boy = 10 + 2 × 42
    12

    Correct Option: B

    According to question ,
    Total increase = 2 × 42

    Age of new boy = 10 + 2 × 42 = 17 years
    12