The square of two digit no. is divided by half the no. After 36 added to the quotient,this sum is then divided by 2.the digits ao the resulting number are same as the original one but in the reverse order.How many numbers fulfill the same criteria?

(a)2 (b)4 (c)6 (d)7

• d) 7
  
  Let no be (10x + y)
  
  1st step => (10x+y)^2 / (1/2)*(10x+y) = 2*(10x+y) = 20x+2y
  2nd step => (20x + 2y + 36)/2 = 10x + y + 18
  
  => 10x + y + 18 = 10y + x
  => 9(y-x) = 18
  => y - x = 2
  => (x,y) = (1,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)
  => 7 possibilities
• 11 years agoHelpfull: Yes(124) No(2)
• 2(10x+y)^2/(10x+y)=10y+x
  10x+y+18=10y+x
  9x-9y+18=0
  9(x-y)=-18
  x-y=-2
  y-x=2
  here (x,y)=(1,3),(3,5),(2,4),(4,6),(5,7),(6,8),(7,9)
  so, there are 7 possibilities only..!
• 9 years agoHelpfull: Yes(4) No(0)
• first we take equation
  ((ab*ab)/(ab/2) +36)/2=ba
  then we get
  ab+18 =ba
  1) 13+18=31
  2) 24+18=42
  3) 35 + 18=53
  4) 46 + 18=64
  5) 57 + 18=75
  6) 68 + 18=86
  7) 79 + 18=97
  
  there are total 7 ways.
  
• 8 years agoHelpfull: Yes(1) No(0)
• d) 7
  
  Let no be (10x + y)
  
  1st step => (10x+y)^2 / (1/2)*(10x+y) = 2*(10x+y) = 20x+2y
  2nd step => (20x + 2y + 36)/2 = 10x + y + 18
  
  => 10x + y + 18 = 10y + x
  => 9(y-x) = 18
  => y - x = 2
  => (x,y) = (1,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)
  => 7 possibilities
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• 10 years agoHelpfull: Yes(0) No(2)