A pencil cost rs. 0.25 ,a pen cost rs. 10 and a book cost rs. 25 .How many each,one should buy so that the total no. of article is 100 and the total amount is rs. 1000?

• There are three solutions.
  
  Number of pencils = C Number of books = B Number of Pens = P
  
  Total Number of articles = 100 = C + P + B
  C = 100 – P - B -- equation 1
  
  Total Purchase:
  
  0.25 * C + 10 P + 25 * B = 1,000 , multiply by 4
  C + 40 P + 100 B = 4,000 --- equation 2
  
  From the above equations, we can infer that maximum value of P is 100, maximum value of B is 40 and Maximum value of C is 100. Minimum of any of them is 1. If the values are more than those maximum then equation 1 or 2 will not be satisfied.
  
  As C + 40 P + 100 B = 4,000 , substitute value of C from equation 1
  100 - P - B + 40 P + 100 B = 4,000
  39 P + 99 B = 3900 divide by 39
  
  P + (33/13) B = 100 -- equation 3
  
  Here, 100 is an integer. P is an integer. So (33 B/13) is also an integer.
  So B = 13, 26, or 39 only three possibilities.
  
  1) B = 13, P + 33 = 100, P = 67
  C = 100 - 13 - 67 = 20.
  Total purchase = 20*0.25 +10*67 + 13*25 = Rs 1,000
  
  2) B = 26, P + 33 * 26/13 = P + 66 = 100, P = 34
  C = 100 - 26 - 34 = 40
  Total purchase = 40*0.25+10*34+25*26 = Rs 1,000
  
  3) B = 39 , P + 99 = 100, P = 1
  C = 100 - 39 - 1 = 60
  total purchase = 60*0.25 + 1 * 10 + 39 * 25 = Rs 1,000
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