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Thread: very very simple puzzle

  1. #1
    Expert Member
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    May 2009
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    Smile very very simple puzzle

    Hi guys,


    Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards.

    Last year, each of them discovered that every tree in their own orchard bore
    exactly the same number of apples.

    Further, if the third farmer gives one apple tothe first,

    & the fifth gives three to each of the second and the fourth

    They would all have exactly the same number of apples.

    Then guys...............


    What were the yields per tree in the orchards of the third and fourth farmers?

    Try u r best...

    All t best.

    Thanks & Regards,

    Riju.


  2. #2
    Contributing Member
    Join Date
    May 2009
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    49

    Lightbulb Re: very very simple puzzle

    1) All trees of a single farmer bore equal number of fruits i.e say 1st farmer has 7 trees and each tree bears 'a' number of fruits. Therefore 1st farmer will have 7a apples.

    2) Similarly 2,3,4,5 farmers will have 9b,11c,13d,14e apples respectively.

    3)Now third farmer gives one apple to the first
    Hence 11c-1 = 7a+1
    Also the fifth gives three to each of the second and the fourth
    Hence 14e-6=9b+3=13d+3

    4) Since after doing this all have exactly the same number of apples
    we can say 14e-6=7a+1
    Thus 14e-7a=7 i.e. 2e-a=1

    Now put a=17 Thus e=9
    5) Now put the above values in step 3, we get c=11, d=9, b=13
    Thus a=17, b=13, c= 11, d= 9, e=9.

    These are the apples yielded per tree for each farmer. If you put these values in step 3, you'll see that each farmer will have 120 apples.

    Don't forget to confirm the answer, Rijus


  3. #3
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    May 2009
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    Re: very very simple puzzle

    Dear vcite,

    U r absltly right.

    The Third & fourth farmer will yeild 11 & 9 apple trees.

    Congrats !!!!!!!

    Absltly Brilliant ............

    Keep it up...



    Thanks & Regards,
    Riju.


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