Question

Sum of the digits of a two_digits number is 9. When we interchanged the digit the digits, it is found that the resulting new number is greater than the original number by 27 . what is the two _ digit number​

Answer 1

let a two digit number be 10x+y

a.t.q.

x+y=9__i

and on interchanging digits it will

10y+x.

then

10x+y+27=10y+x.

9x=9y-27.

x=y-3. ____ii

but x=9-y. (from___I)

put in __,ii

9-y=y-3

12=2y

y=6.

x=6-3

x=3.

hence the original number is 10×3+6

= 36.