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 digits is 1 less than middle digits. find the number

100x+10y+z= 17(x+y+z)......... (1)
100x+10y+z+198= 100z+10y+x...........(2)
from (2) we get
99(z-x)= 198
z-x= 2
z= x+2.......... (3)
now
z+x= y-1 (given)
2x+3=y........ (4)
putting (3) and (4) in (1) we get
100x+ 10(2x+3) + x+2= 17(x+2x+3+x+2)
by solving we get x=1
z=1+2=3
y=2+3=5
so the required number is 100+50+3= 153....... [ans]