Problem Based on ages


  1. The sum of the ages of a daughter and mother is 56 years. After 4 years, the age of the mother will be 3 times that of the daughter. Their respective ages are.









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    Suppose the age of mother be P years and that of daughter’s age be Q years.
    According to question P + Q = 56 .........(i)
    After 4 years, P + 4 = 3 (Q + 4) ⇒ P + 4 = 3Q + 12 ⇒ P – 3Q = 8 ......(ii)

    Correct Option: B

    Suppose the age of mother be P years and that of daughter’s age be Q years.
    According to question P + Q = 56 .........(i)
    After 4 years, P + 4 = 3 (Q + 4) ⇒ P + 4 = 3Q + 12 ⇒ P – 3Q = 8 ......(ii)
    On solving equations (i) and (ii) , we get
    Q = 12 years
    ∴ P = 56 – 12 = 44 years
    Hence , the age of mother is 44 years and her daughter’s age is 12 years .


  1. Ravi is younger to his brother by 3 years. At the time of birth of his sister the age of his father was 28 years and that of his mother was 26 years. The age of his sister was 4 years at the time of birth of his brother. What was the age of his father at the time of the birth of Ravi?









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    The age of sister of Ravi at the time of birth of Ravi’s brother = 4 years
    Ravi’s sister is 4 + 3 = 7 years elder than Ravi.

    Correct Option: B

    The age of sister of Ravi at the time of birth of Ravi’s brother = 4 years
    Ravi’s sister is 4 + 3 = 7 years elder than Ravi.
    The age of father at the time of birth of Ravi = 28 + 7 = 35 Years



  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?









  1. View Hint View Answer Discuss in Forum

    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. 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?









  1. View Hint View Answer Discuss in Forum

    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. 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 .