Question

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 ?

A) 17 & 9 B) 9 & 11 C) 9 & 9 D) 11 & 9

Answer 1

D) The yields per tree in the orchards of the 3rd & 4th farmers ⇒ 11 & 9

Given :

Just let, b, c, d, and e represent the number of apples in each of the five farmers' trees. As a result, the total number of apples is 7a, 9b, 11c, 13d, and 14e.

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

$9b+3 = 13d+3$      ⇒ Here 3 is common

After Cancelation common elements,

   $9b = 13d$

   $b = 13 , d = 9$

Substitute b & d values ⇒ $9b+3 = 9*13+3 = 120$

   Here, $x=120$

After substituting x values,  

3rd Former,

$11c-1 = 120\\11c = 121\\c=11$

4th Former,

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

Tends to produce per tree in 3rd and 4th farmers  = 11 & 9

Answer 2

Answer:

9 and 11

Step-by-step explanation:

The second and fourth farmers have equal number of apples after they got 3 apples each. So, they would have had equal number of apples before getting 3 apples also. Now LCM of 9 and 13 is 117. So they had 117 apples each originally, since yield per tree is same. Now after receiving apples they have 120 apples, and in fact every farmer has 120 apples.

Yield per tree of fourth farmer = 117/13 = 9

Third farmer also has 120 apples after giving 1 apple away, so originally must have had 121 apples

Yield per tree of third farmer = 121/11 = 11