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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 yields exactly the same number of apples. Further, if the 3rd farmer gives one apple to the 1st and the 5th gives 3 to each of the 2nd & d 4th, they would all exactly have the same number of apples, what were the yields per tree in the orchards of the 3rd & 4th farmers ?

Correct Answer: 11 & 9

Let the number of apples in each tree of the 5 farmers be a, b, c, d,e respectively. Therefore total no of apples are 7a, 9b, 11c, 13d and 14e respectively.

Given, 7a+1 = 9b+3 = 11c-1 = 13d+3 = 14e-6 = x

9b+3 = 13d+3===> 9b = 13dso take b = 13 and d = 9

9b+3 = 9*13+3 = 120 ie, x=120

substituting7a+1 = 1207a = 119a = 17

11c-1 = 12011c = 121c=11

14e-6 = 12014e = 126e = 9

Yields per tree in the orchards of d 3rd & 4th farmers= 11,9

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