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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

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

Grade:10

1 Answers

Shashank Singh
askIITians Faculty 57 Points
6 years ago
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]

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