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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 to the first, and the fifth gives three to each of the second and the fourth, they would all have exactly the same number of apples. What were the yields per tree in the orchards of the third and fourth farmers?
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 Answer
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11 & 9 apples per tree.Explanation:Let a, b, c, d & e be the total number of apples bored per year in A, B, C, D &E ?s orchard. Given that a + 1 = b + 3 = c - 1 = d + 3 = e - 6But the question is to find the number of apples bored per tree in C and D ?s orchard.If is enough to consider c - 1 = d + 3.Since the number of trees in C?s orchard is 11 and that of D?s orchard is 13.Let x and y be the number of apples bored per tree in C & d ?s orchard respectively.Therefore 11 x - 1 = 13 y + 3By trial and error method, we get the value for x and y as 11 and 9.
7+9+11+13+14
8+12+11+16+2
9.8
Hence they have
Answered By: Parul Date: 4/24/2008
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