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?

• 11,9 ans
  
  let total apple on tree A,B,C,D,E are a,b,,d,e respectively
  according to question
  a+1 = b+3 = c-1 = d+3 = e-6
  
  consider
  c-1 = d+3
  as C farmer has 11 trees therefore c is a multiple of 11 in same way d is a multiple of 13
  
  11x-1 13y+3
  by putting sme values we get
  
  x=11,y=9
  
  so after all transction of apples every farmer has 120 apples
  
  a=119, yields per tree 119/7 = 17
  b=117 yields per tree 117/9 =13
  c=121 yields per tree 121/11 = 11
  d=117 yields per tree 117/13 = 9
  e=126 yields per tree 126/14 = 9
• 11 years agoHelpfull: Yes(12) No(3)
• 11 & 9 apples per tree.Explanation:Let a, b, c, d & e be the total number of apples bored per year in A, B, C, D &E ?s orchard. Given that a + 1 = b + 3 = c - 1 = d + 3 = e - 6But the question is to find the number of apples bored per tree in C and D ?s orchard.If is enough to consider c - 1 = d + 3.Since the number of trees in C?s orchard is 11 and that of D?s orchard is 13.Let x and y be the number of apples bored per tree in C & d ?s orchard respectively.Therefore 11 x - 1 = 13 y + 3By trial and error method, we get the value for x and y as 11 and 9.
• 8 years agoHelpfull: Yes(0) No(0)