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Mother Daughter age puzzle

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Ten years back the age of the mother was 4 times of her daughter’s age
and
After ten years – mother’s age is two times of her daughter’s age,

what is the present age of the daughter?

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Detective Expert Asked on 3rd September 2015 in Math Puzzles.
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    • 2 Answer(s)

    If we interpret the meaning of: “After ten years”.. 10 years from now then the answer is M=50 AND D=20, here  10 years ago M=50-10 =40 and D-10=10 is ===> (M=D*4),  and 10 years from now M=50+10 =60, D+10=20+10 =30 so M*2D.
    But if it means after the first situation which brings it to present time then the answer will be M=30 D=15 (M-10 = 30-10 = 20 = (D-10 = 15-10 =5) *4, & M=30 = 2*D(=15)

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    Moshe Expert Answered on 28th December 2022.
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    Answer,
    Present age of MOTHER = 50
    And
    DAUGHTER = 20

    EXPLANATION-
    Lets Mother’s Age be M
    and Daughter’s agr be D

    So,
    Given
    (M-10) = 4(D-10)      –   I
    and
    (M+10) = 2(D+10)         –     II

    Solving both equation,

    M = 4D-30 (From I)        –    III

    In Equ II-
    4D-20=2D+20
    2D=40
    D=20

    and substituting in III
    M=50

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    SherlockHolmes Expert Answered on 3rd September 2015.

    mathman

    Daughter being 20, and mother being 50, that is NOT correct, as 20 x 2 does NOT = 50.  If you take 10 years away, them being 10 / 40, that DOES make the 4x part of the equation valid, however 20 / 50 does NOT make the 2x part of the equation valid.   Try the daughter being 15 now, mother 30 (15 x 2 = 30), and ten years ago, daughter being 5, mother being 20 (5 x 4 = 20).   So the daughter is now 20 (mother now 40).

    on 14th January 2016.
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    mathman

    20 / 50 is incorrect, as 20 x 2 does NOT = 50.    The daughter is 15 now (mother 30), 15 x 2 = 30.   10 years ago, daughter 5, mother 20, 5 x 4 = 20.  So the daughter is 15 now.

    on 14th January 2016.
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    Moshe

    It depends how you interpret the meaning of: “After ten years”.. If it means 10 years from now then the answer is correct because in M=50 AND D=20 so 10 years ago M=50-10 =40 and D-10=10 is correct (M=D*4),  and 10 years from now M=50+10 =60, D+10=20+10 =30 so M*2D, But if it means after the first situation which brings it to present time then the answer will be M=30 D=15

    on 28th December 2022.
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