SOLUTION: The sum of the digits of a three-digit number is 18. If the second and third digits were interchanged, the number would be increased by 36. If the first and third digits were inter

Question 634364: The sum of the digits of a three-digit number is 18. If the second and third digits were interchanged, the number would be increased by 36. If the first and third digits were interchanged, the new number would be 99 less than the original number. Find the number.
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
The sum of the digits of a three-digit number is 18. If the second and third digits were interchanged, the number would be increased by 36. If the first and third digits were interchanged, the new number would be 99 less than the original number. Find the number.

ans:
let the digits be x,y,z at hundreds,tenths& ones place
as per question x+y+z=18 -eqn 1
the no be 100x+10y+z
if the second and third digits were interchanged than
the no will be 100x+10z+y
as per question 100x+10z+y=100x+10y+z+36
or 9(z-y)=36
or z-y=4 ----eqn 2
If the first and third digits were interchanged
the no will be 100z+10y+x
as per question 100z+10y+x=100x+10y+z-99
or 99(x-z)=99
or x-z=1 ----eqn 3
adding eqns 1& 2 we get x+2z=22--eqn 4
from eqn 4 & 3 3z=21
or z=7
from eqn 4 x=22-2*7=8
from eqn 1 y=18-8-7=3
so the no is 837 ans

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