Question

the sum of digits in a two digit number is 9 if 27 subtracted from the number digits of the number are interchanged find the original number

Answer 1

Answer:

Step-by-step explanation:

let the number be 10x + y

so 10x + y -27 = 10y + x

9x -9y =27

x-y = 3

x + y =9

x = 6

y =3  

the number is 63

Answer 2

Let the original number be 10x + y
And the interchanged number be 10y + x
Given,
x+y=9...eq(1) and (10x+y)-(10y+x) =27
=> 10x+y-10y-x=27
=>9x-9y=27
=>9(x-y)=27
=>x-y = 27/9 =3
=>x-y=3...eq(2)
eq(1) + eq(2)
x+y=9
x-y =3
————
2x+0y=12
=>x=6
Now substitute x value in eq(1)
6+y=9
=>y=3
Thus the number is
63