Question

the sum of the digit of a two digit number is 9.If 27 is added to the number, the digit interchange their place.Find the number.

Answer 1

let the unit digit be x
Then the tens digit be =(9-x)
The original number =10×(9-x)+x
=90-10x+x
=90-9x
After interchange the digit
The new number =10×x+(9-x)
=9x+9
According to the question
9x+9=90-9x+27
9x+9x=90+27-9
18x=108
X=108/18=6
So the number =90-9×6=36

Answer 2

Let the unit place be x
Then tens place will be 9-x
Number=10 x (tens place) + ones place
=10 x( 9-x)+x
=90-10x+x
=90-9x
New no. after adding 27=10x+9-x
=9x+9
given that,
90-9x+27=9x+9
90+27-9=9x+9x
108=18x
108/18=x
x=6
:.unit place digit=6
tens place digit=9-6=3
original no.=36