The number obtained by interchanging the two digits of a two digit number is lesser than the original number by 54. If the sum of the two digits of the number is 12, then what is the original number?
(1) 28
(2) 39
(3) 82
(4) Can’t say
(5) None of these

• (5) None of these
  
  Let with two digits x and y, original number= 10x+y
  Number obtained by reversing the digits= 10y+x
  Given the later number is less by 54 than the original, so 10x+y -(10y+x)=54 or x-y=6 ---(i)
  Also Sum of the two digits is 12, so x+y= 12 ----(ii)
  From (i) & (ii), x=9, y=3
  So original number=10x+y= 10*9 +3= 93
• 7 years agoHelpfull: Yes(5) No(0)
• Let ten's digit= x
  Unit's digit= 12-x
  
  A/Q;
  
  [10(12-x)+x] - [10x + (12-x)]= 54
  
  On solving, we get;
  
  x=3.
  
  So, ten's digit= 3
  Unit's digit= 9
  
  Thus the original number is 39..
• 6 years agoHelpfull: Yes(1) No(0)
• 93
  
  10x+y-10y-x=54
  and x+y=12
• 7 years agoHelpfull: Yes(0) No(0)
• Let with two digits x and y, original number= 10x+y
  Number obtained by reversing the digits= 10y+x
  Given the later number is less by 54 than the original, so 10x+y -(10y+x)=54 or x-y=6 ---(i)
  Also Sum of the two digits is 12, so x+y= 12 ----(ii)
  From (i) & (ii), x=9, y=3
  So original number=10x+y= 10*9 +3= 93
  they asked interchanged digit correct ans 39
• 6 years agoHelpfull: Yes(0) No(0)
• 5
  
  Let with two digits x and y, original number= 10x+y
  Number obtained by reversing the digits= 10y+x
  Given the later number is less by 54 than the original, so 10x+y -(10y+x)=54 or x-y=6 ---(i)
  Also Sum of the two digits is 12, so x+y= 12 ----(ii)
  From (i) & (ii), x=9, y=3
  So original number=10x+y= 10*9 +3= 93
• 4 years agoHelpfull: Yes(0) No(0)