Answer:
93
Step-by-step explanation:
Let the digit in tens place be 'x' & digit in ones place be 'y'.
So , the original number = [tex]10x+y[/tex]
According to the question , [tex]x+y=12[/tex]......... .eqn(1)
When digits are interchanged ,
The new number formed = [tex]10y+x[/tex]
According to the question , [tex]10y+x=10x+y-54[/tex] ............ eqn(2)
Solving eqn(2) further ,
[tex]10y+x=10x+y-54\\=>10x-x-10y+y=54\\=>9x-9y=54\\=>9(x-y)=54\\=>x-y=\frac{54}{9}=6.......... eqn(3)[/tex]
Adding eqn(1) and eqn(3) ,
[tex](x+y)+(x-y)=12+6\\=>x+y+x-y=18\\=>2x=18\\=>x=\frac{18}{2} =9[/tex]
Putting the value of x in eqn(1),
[tex]9+y=12\\=>y=12-9=3[/tex]
∴ Original number = 93
