Question

the sum of the digit of a 2-digit number is 15.if the number formed by
reversing a digit is less than the original number by 27,find the original number.

Answer 1

Let the digit at ones place be x and digit at tens place be y.
Therefore, Number=10y+x
x+y=15---------(i)
10x+y=10y+x-27
9x-9y=-27
x-y=-3----------(ii)
Add (i) and (ii),
Therefore,2x=12
x=6
6+y=15
y=9
So, the number is 10(9)+6=96.

Answer 2

let the no be 10x+y
and sum be x+y=15 ---(1)
on interchanging the digit the no become
10y+x
so, 10y+x=10x+y-27
9x-9y=-27
x-y= -3
y=x-3
putting the value in (1)
x+x-3=15
2x=18
x=9
and, y= 6
the number is 96