Latest CTS Aptitude Question SOLUTION: 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 d same no of apples.

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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 d same no of apples.further,if d 3rd farmer gives one apple to the 1st,& the 5th gives 3 to each of the 2nd & d 4th,they would all exactly have the same no of apples, what were d yields per tree in the orchards of d 3rd & 4th farmers?

Asked In CTS souvik das (10 years ago)

Solved Saraswathy Read Solution (3)

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Ann Theressa  (10 years ago)

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 = 13d
so take b = 13 and d = 9

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

substituting
7a+1 = 120
7a = 119
a = 17

11c-1 = 120
11c = 121
c=11

14e-6 = 120
14e = 126
e = 9

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

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Saraswathy  (10 years ago)

11 & 9 apples per tree.

Let a, b, c, d & e be the number of apples bored last year in each farmer's tree.

Given that 7a + 1 = 9b + 3 = 11c - 1 = 13d + 3 = 14e - 6
But the question is to find the number of apples bored per tree in 3rd nd 4th orchard.It is enough to consider 11c - 1 = 13d + 3..


Therefore 11 c - 1 = 13 d + 3
By trial and error method, we get the value for c and d as 11 and 9.

5th nd 4th

14e - 6 = 13d + 3
14e - 13d = 9

here if u put e=d=1, result ll be 1, e=d=2 difference ll be 2, .... e=d=9 ,result ll be 9

so e=9 , d=9
So 5ht tree ll give 14 * 9 = 126 no. of apples
4th tree ll give 13 * 9 = 117 no. of apples

for 5th nd 2nd
14 * 9 -6 = 9 * b + 3
120=9b + 3
b = 13

So 2nd tree ll give 9 * 13 = 117

A= 119 , per tree = 17
B= 117 , per tree = 13
C= 121, per tree = 11
D= 117, per tree = 9
E = 126 , per tree = 9

3'rd farmer have 11 apples per tree and

4'th farmer have 9 apples per tree.

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pragada santhosh  (10 years ago)

11,9
approach this pblm in this manner.

since given every tree in their own orchard yields same no of apples
then take
each tree of 1st farmer 'a' fruits
2nd 'b'
so on



Thn 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 = 13d
so take b = 13 and d = 9

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

substituting
7a+1 = 120
7a = 119
a = 17

11c-1 = 120
11c = 121
c=11

14e-6 = 120
14e = 126
e = 9

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

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