Oranges can be packed in sets of 10 oranges in box type A or 25 oranges in box type B. A carton
comprising of 1000 oranges of type a and b is packed. How many different combinations are possible in the
number of type A and type B boxes while organizing the oranges?

• 21
  
  Let number of type A box=a and type B box=b, then 10a + 25b = 1000
  Possible combinations of (a,b) are (0,40), (5,38), (10,36), ..... (100,0) which forms an A.P.
  Here number of possible combinations are the number of terms of any of the A.P. series.
  Consider, series 0, 5, 10, ...., 100 where a=0, d=5, number of terms=n, then Last term=a+(n-1)d
  => 100=0+(n-1)5
  5n=105
  n=21
  Therefore, different possible combinations with type A and type B boxes are 21.
• 4 years agoHelpfull: Yes(13) No(5)
• the prev sol. is wrong...guys dont do that
• 4 years agoHelpfull: Yes(3) No(7)
• The expression will be 10x+25y=1000 ----------(1)
  The exp (1) satisfied only with multiples of 2 up to 38.
  so no. of combinations are 19.
  if oranges are packed in type A boxes only= 1 way
  if oranges are packed in type B boxes only= 1 way
  Hence total = 19+1+1 = 21
• 4 years agoHelpfull: Yes(2) No(0)
• 21 combinations
  A B
  0 40
  5 38
  10 36
  . .
  . .
  95 2
  
  when you count the total possible number is 21
• 4 years agoHelpfull: Yes(1) No(0)
• 201
  
  Let number of type A box=a and type B box=b, then 10a + 25b = 1000
  Possible combinations of (a,b) are (0,40), (5,38), (10,36), ..... (100,0) which forms an A.P.
  Here number of possible combinations are the number of terms of any of the A.P. series.
  Consider, series 0, 5, 10, ...., 100 where a=0, d=5, number of terms=n, then Last term=a+(n-1)d
  => 1000=0+(n-1)5
  n-1=200
  n=201
  Therefore, different possible combinations with type A and type B boxes are 201.
• 4 years agoHelpfull: Yes(1) No(9)
• 10a+25b=1000
  lcm(10,25)=50
  ans=(1000/50)+=21
• 3 years agoHelpfull: Yes(1) No(0)
• here total number of oranges are 1000 .so the total no of oranges will be in the form of 10x+25y=1000 as type a oranges can be put 10 ina box and 25 of type b . so on making the algebra easy 10x + 25 y = 1000 can be written as x = 1000 - (25/10)y . which is also x = 1000 -(5/2)y. here y should be multiple of 2 and the product should be atmost 100.tus our combination starts from 0 ,2,4,6 ....to 20.now doing ap for total no of combinations we get 20=0+(n-1)2. n=11
• 4 years agoHelpfull: Yes(0) No(3)
• no of A type boxes=40
  No of B type boxes =1
  So there will be 40 ways...select box of type A and the type B
• 4 years agoHelpfull: Yes(0) No(0)
• 1st combination A0 B40
  Last combination A100 B0
  Difference in A.p of A =5
  No. Of combination=21
• 4 years agoHelpfull: Yes(0) No(0)