Question

The number obtained by interchanging the digits of a two digits number is more than the original number by 27. if the sum of the dogits is 13, then what is the original number

Answer 1

Let the tens digit be x and the units digi be y.
So the number=10x+y
A.q. (x+y)=13
x=13-y (equation 1)
After inter changing the number
=10y+x
Also,
(10y+x)-(10x+y)=27
10y+x-10x-y=27
9y-9x=27
9(y-x)=27
y-x=27/9
y-x=3
From equation 1 x=13-y
So,y-(13-y)=3
y-13+y=3
2y=13+3
2y=16
y=16/2
y=8
And, x=13-y
=13-8
=4
Hence the number is 48.