The sum of the digits of a three digit number is 17, and the sum of the squares of its digits is 109. If we subtract 495 from that number, we shall get a number consisting of the same digits written in the reverse order. Find the number

• ans will be 863
  sum of the digits= 8+6+3=17
  sum of the squares = 64+36+9 = 109
  863-495=368
• 11 years agoHelpfull: Yes(22) No(2)
• Its better if we do option verification.
  The answer could be 863.
  coz we have x+y+z=17
  100x+10y+z-495=100z+10y+x ie x-z=5
  using this we can have
  2z+y=12, by trial and error we have 863
• 11 years agoHelpfull: Yes(17) No(1)
• Let the digits be a,b,c
  Given 100a+10b+c=17
  and a^2 + b^2 +c^2 =109 --eq (2)
  and also 100a+10b+c-495 = 100c+10b+a
  => 99a-99c=495
  => a-c=5
  => a=5+c
  take c=1 , so a=6 then b will be 10 which is impossible.
  take c=2, so a=7 and b=9 and substitute in eq (2), its not satisfied.
  take c=3, so a=8 and b=5 and eq(2) will be 8^2 + 5^2 + 3^2 =109 and also satisfies the given conditions..
  so, the number is 853
  
• 11 years agoHelpfull: Yes(4) No(8)
• x+y+z=17 ---(1),
  x2+y2+z2=109 -----(2),
  100x+10y+z-495=100z+10y+x
  x-z=5 -----(3)
  solving 1,2,3 we get x=8,y=6,z=3
• 11 years agoHelpfull: Yes(3) No(0)
• given,
  100x+10y+z-495=100z+10y+x
  x-y=5
  solve it from the option that first and the last digit has the difference of 5
• 11 years agoHelpfull: Yes(2) No(0)
• Sorry friends ..Itz mistyped.. the answer is 863 only..
• 11 years agoHelpfull: Yes(1) No(0)
• let, three numbers be x,y,z
  x+y+z=17
  x2 +y2+z2=109
  now,
  495-109=386.
  but it is reverse in order.
  therefore,
  x=6,y=8,z=3
  ie x+y+z=6+8+3=17
• 8 years agoHelpfull: Yes(1) No(0)
• Go with Option.. 773 , 944, will not be 109 when added their squares.
  for 863,
  8+6+3=17,
  sqrs: 64+36+9=109,
  495-109=386. when we reversed 863 it will be 368.
  So the correct answer is 683. if we reversed it we get 386.
  ans= 683
• 8 years agoHelpfull: Yes(0) No(0)
• go or option veriation it is very much simple rather than solvin
• 8 years agoHelpfull: Yes(0) No(0)
• The ans is 863
• 8 years agoHelpfull: Yes(0) No(1)