Analytical - Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards. Last year, each of

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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?

Total Answers and Comments: 4

Last Update: March 21, 2007 Asked by: praveenkumar rudra

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Best Rated Answer

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Submitted by: pkoshti

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.

Above answer was rated as good by the following members:
karthika reddy

September 28, 2006 09:27:40

tarun singh

RE: Five farmers have 7, 9, 11, 13 & 14 apple trees, r...

3rd farmer 11apple each

4th 9 apple each

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November 25, 2006 07:52:37

madhu mechanical

RE: Five farmers have 7, 9, 11, 13 & 14 apple trees, r...

answer are 10

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February 17, 2007 03:24:47

pkoshti

RE: Five farmers have 7, 9, 11, 13 & 14 apple trees, r...

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.

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1 0

Overall Rating: +1

March 21, 2007 12:03:30

mayank

RE: Five farmers have 7, 9, 11, 13 & 14 apple trees, r...

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.

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