The ratio of the number of apples to oranges to pears is 7:11:9.
Timmy ate 21 fruits.
As a result, the ratio of the number of apples to oranges to pears
became 2:3:3. How many fruits were left ?

• ans is 168
  27x-21=8y
  verify above expression with x=1,3,5,7....
  and the lowest value of x which satisfies the equation is 7
  so, 27(7)-21=168(MULTIPLE OF 8)
• 11 years agoHelpfull: Yes(48) No(1)
• Since we won't be dealing in fractions here, the total number of fruits
  to begin with (B) must be a multiple of 7+11+9 = 27 and after Timmy pigs
  out, a multiple of 8 (A). That is because 7, 11, and 9 have no common
  factors, nor do 2 and 3.
  
  Let B = 27 b and A = 8 a.
  
  27b - 21 = 8a
  We need to solve this Diophantine Equation in integers.
  
  b = (8a + 21)/27
  
  27 = 3 × 3 × 3, so 8a + 21 must be divisible by 3,
  21 is a multiple of 3, so 8a must also be a multiple of 3.
  Therefore a must be a multiple of 3.
  
  Trying various multiples of 3, we find that the lowest value of a that
  makes this come out in integers is 21.
  
  (There are better ways of doing this, but in this case the slow method
  works because the numbers are small enough.)
  
  a = 21, means there were 168 fruits left (8a):
  42 apples, 63 oranges, 63 pears (2a, 3a, 3a)
  adding the 21 fruits Timmy ate, makes 189 fruits
  189/27 = 7, so b = 7
  49 apples, 77 oranges, 63 pears. (7b, 11b, 9b)
  He ate 7 apples, 14 oranges, and 0 pears.
  
• 11 years agoHelpfull: Yes(14) No(15)
• @GAURAV JAISWAL Please Post the correct answer if you have.
• 11 years agoHelpfull: Yes(5) No(1)
• Let the initial total fruits based on the ratio be 27 k(7k+11k+9k0
  
  The final total fruits be 8 m(2m+3m+3m)
  
  We know 27 k - 8 m = 21, now we have to try trail and error, as 8m is always even, 27 k should be odd, so try k = 1,3,5,7 and so on.
  
  The values match when k=7 and m = 21
  
  So, initial fruits are 189 and final fruits are 168
• 11 years agoHelpfull: Yes(3) No(0)
• i think the answer will be 168 because question asked is how many fruits left and not who ate how much
• 11 years agoHelpfull: Yes(2) No(5)
• ans is 8
  couse the total ratio of the fruts is 2:3:3
  so by adding it 2+3+3=8
  therefore the ans becomes 8
• 10 years agoHelpfull: Yes(0) No(8)