Problem Based on ages


  1. The average weight of 8 persons of a family is increased by 1 kg when one of the members whose weight is 60 kg is replaced by a new person. The weight of the new person (in kg) is









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    Here , n = 8 , Weight of replaced person = 60 kg and increase in Average = 1 kg
    Using formula ,
    ∴ Weight of new person = Weight of replaced person + n × increase in Average

    Correct Option: B

    Here , n = 8 , Weight of replaced person = 60 kg and increase in Average = 1 kg
    Using formula ,
    ∴ Weight of new person = Weight of replaced person + n × increase in Average
    Weight of new person = 60 + 8 × 1 = 68 kg


  1. At present a father’s age is 30 years more than that of his only son. What was his age when the son was born?









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    Suppose the age of son at present = P years
    ∴ Present age of the father = Present age of son + 30 years
    Present age of the father = P + 30 years

    Correct Option: B

    Suppose the age of son at present = P years
    ∴ Present age of the father = Present age of son + 30 years
    Present age of the father = P + 30 years
    Age of father at the birth of his son = Present age of the father - Present age of son = ( P + 30 ) – P = 30 years



  1. The average age of 19 boys in a class is 21 years. If the teacher’s age is included, the average increases to 22 years. What is the teacher’s age?









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    Given that :- The average age of 19 boys in a class = 21 years
    Total age of 19 boys = 19 × 21 = 399 years
    The average age of 19 boys and teacher = 22 years
    Total age of 19 boys and teacher = 20 × 22 = 440 years

    Correct Option: B

    Given that :- The average age of 19 boys in a class = 21 years
    Total age of 19 boys = 19 × 21 = 399 years
    The average age of 19 boys and teacher = 22 years
    Total age of 19 boys and teacher = 20 × 22 = 440 years
    ∴Teacher’s age = Total age of 19 boys and teacher - Total age of 19 boys
    Teacher’s age = 440 – 399 = 41 years
    Hence , the age of teacher is 41 years .


  1. 10 years ago, average age of A and B was 20 years. Average age of A, B and C is 30 years today. How old C will be after 5 years?









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    Let the present ages of A, B and C be P years, Q years and R years respectively.
    According to question,
    Ten years ago, average age of A and B = 20 years.

    (P - 10) + (Q - 10)
    = 20
    2

    Correct Option: C

    Let the present ages of A, B and C be P years, Q years and R years respectively.
    According to question,
    Ten years ago, average age of A and B = 20 years.

    (P - 10) + (Q - 10)
    = 20
    2

    ⇒ P – 10 + Q – 10 =40
    ⇒ P + Q = 60 .....(i)
    Average present age of A, B and C = 30 years
    Again,
    P + Q + R
    = 30
    3

    ⇒ P + Q + R = 30 × 3 = 90 ....(ii)
    On solving equations (i) and (ii) , we get
    R = 30 years
    Hence, the age of C after 5 years = 30 + 5 = 35 years



  1. A father is 3 times as old his son. 8 years ago, the father was 5 times as old as his son. What is the present age of the son?









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    Suppose the present age of the son is P years.
    Therefore, the present age of father will be 3P years.
    According to question , Eight years ago, 5 × ( the present age of the son - 8 years ) = ( the present age of father - 8 years )
    5(P – 8) = 3P – 8
    ⇒ 5P – 40 = 3P – 8
    ⇒ 5P – 3P = 40 – 8
    ⇒ 2P = 32

    Correct Option: C

    Suppose the present age of the son is P years.
    Therefore, the present age of father will be 3P years.
    According to question , Eight years ago, 5 × ( the present age of the son - 8 years ) = ( the present age of father - 8 years )
    5(P – 8) = 3P – 8
    ⇒ 5P – 40 = 3P – 8
    ⇒ 5P – 3P = 40 – 8
    ⇒ 2P = 32

    ∴ P =
    32
    = 16 years
    2

    Therefore , the present age of the son is 16 years.