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?

• 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
  
• 10 years agoHelpfull: Yes(38) No(0)
• 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.
• 10 years agoHelpfull: Yes(25) No(0)
• 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....
• 10 years agoHelpfull: Yes(1) No(0)