How old are Daniel and Jessica now?

1,408.3K Views

Alan’s son Daniel, is exactly one fifth of Alan’s age.

In 21 years time, Alan will be exactly twice Daniel’s age.

Betty’s is exactly seven times the age of her daughter, Jessica.

In 8 years time, Betty will be three times the age of Jessica.

How old are Daniel and Jessica now?

Share
Add Comment

  • 1 Answer(s)

    Daniel is 7 years old and Jessica is 4 years old.

    The first half of the question involves Daniel (D) and Alan (A).

    Daniel is currently one fifth of Alan’s age, so:

            A = D x 5           (1)

    In 21 years time, Alan will be twice his age, so:

       A + 21 = (D + 21) x 2    (2)

    Using (1) in (2) gives:

       A + 21 = (D + 21) x 2

      5D + 21 = (D + 21) x 2

      5D + 21 = 2D + 42

           3D = 21

            D = 7

    So Daniel is 7 (and Alan is 35).

    The second half of the question involves Jessica (J) and Betty (B).

    Betty’s is exactly seven times the age of Jessica:

            B = J x 7           (3)

    In 8 years time, Betty will be three times the age of Jessica, so:

        B + 8 = (J + 8) x 3     (4)

    Using (3) in (4) gives:

        B + 8 = (J + 8) x 3

       7J + 8 = (J + 8) x 3

       7J + 8 = 3J + 24

           4J = 16

            J = 4

    So Jessica is 4 (and Betty is 28). QED.

    pnikam Expert Answered on 25th August 2015.
    Add Comment
  • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.
  • More puzzles to try-