Question

the sum of the digit of a two digit number is 9. the number obtained by interchanging its digit is 9 less than thrice the original number find the number

Answer 1

Let y be the number in one's position and x be in the 100th position
Givem that
x+y=9-----1
2 digit number will be of the form
10x+y
By condition if we interchamge the number ,the new number will be as 10y+x
given that
10y+x=3(10x+y)-9
10y+x=30x+3y-9
29x-7y=9----2
Eqn 1 *7
We get
7x+7y=63----3
Now adding eqn 2 and 3
7x+7y=63
29x-7y=9
___________
36x=72
X=2
from eqn x+y=9
We get y=7
So number is
10x+y= 10*2+7=27