Question

A three digit number is equal to 17 times the sum of its digits. if 198 is added to the number , then the extreme digits get interchanged . the sum of first and third digit is 1 less than middle digit. find the numbers.

Answer 1

Hello..

Let ones digit = x
tens digit = y
hundreds digit = z

number becomes = 100z+10y+x



  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

Hey!!
-----------------
-----------------

Let x,y,and z be the digits:

100x+10y+z=17(x+y+z)

100x+10y+z+198=100z+10y+x
x+z+1=y;

So:
100x+z+198=100z+x
99x+198=99z
x+2=z

x+(x+2)+1=y

y=2x+3
100(x)+10(2x+3)+(x+2)=17(x+2x+3+x+2)

100x+20x+30+x+2=68x+85
53x+32=85
53x=53

x=1,y=5,z=3 Ans.

---------------------
---------------------
I Hope It's Help You......!!!!

please tick the brainliest answer.