Question

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number,the extreme digits get interchanged. The sum of first and third digit is 1 less than middle digit.Find the number..... (please answer fast)

Answer 1

Let ones digit = x  , tens digit = y , hundreds digit = z
So, number becomes = 100z+10y+x
According to question-

  100z+10y+x   =  17(x+y+z)
  100z+10y+x   =   17x + 17y + 17z
  100z-17z +10y-17y + x-17x = 0
   83z -7y -16x = 0                                     -----------------------(1)

Also,
100z+10y+x + 198 = 100x + 10y + z
100z- z +10y-10y +x - 100x +198 = 0
99z - 99x +198 = 0
99x - 99z = 198  
 x - z = 2 
 x = z + 2                                                       ----------------------------(2)

And,  
z + x = y-1
By putting (2)
y = z+z+2+1      
 y = 2z+3                                                        ----------------------------(3)
                 Putting (3) and (2) in (1) we get
 
83z -7(2z+3) -16(z+2) = 0
83z -14z -21 -16z -32  = 0
53z = 53
z = 1
put z = 1 in (3)
y = 2(1) +3
y = 5

Put z = 1 in (2) 
x = 1+3= 3
So. number = 100(1) + 10(5)  + 3 = 153
So, number = 153

Answer 2

here is your answer... the digit in tens place is 3+1+1=5...the no. is 153