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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Sep 27th, 2006
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tarun singh

Sep 28th, 2006

3rd farmer 11apple each
4th 9 apple each

madhu mechanical

Nov 25th, 2006

answer are 10

pkoshti

Feb 17th, 2007

Let no.of apples with all farmers are L,M,N,X,Y respectivly.
According to problem
7L+1 = 9M+3 = 11N-1 = 13X+3 = 14Y-6
After trial & error method I found that...........
L=17,
M=13,
N=11,
X=9,
Y=9,
After putting these values in equation
120=120=120=120=120.
Therefore
3'rd farmer have 11 apples per tree and
4'th farmer have 9 apples per tree.

mayank

Mar 21st, 2007

i have a very simple way... and logically correct too
we see that the 5th farmer gave 3 apples each to 2nd and 4th one ..
this implies that before getting those apples, they still had equal no of apples...

l.c.m of 9 and 13 gives 117
so they had 117 apples each and after getting from 5th.... they had 120 each...

now to verify 5th farmer must have 120+6 =126 apples at first(14*9)
also 1st one had 120-1=119 apples(7*17)
3rd one had 120+1=121 apples(11*11)

so 2nd farmer had 13 apples in each tree
and 4th had 9 apples in each tree.