Question

The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number is

Answer 1

Answer:

93

Step-by-step explanation:

Let the digit in tens place be 'x' & digit in ones place be 'y'.

So , the original number = $10x+y$

According to the question , $x+y=12$......... .eqn(1)

When digits are interchanged ,

The new number formed = $10y+x$

According to the question , $10y+x=10x+y-54$ ............ eqn(2)

Solving eqn(2) further ,

$10y+x=10x+y-54\\=>10x-x-10y+y=54\\=>9x-9y=54\\=>9(x-y)=54\\=>x-y=\frac{54}{9}=6.......... eqn(3)$

Adding eqn(1) and eqn(3) ,

$(x+y)+(x-y)=12+6\\=>x+y+x-y=18\\=>2x=18\\=>x=\frac{18}{2} =9$

Putting the value of x in eqn(1),

$9+y=12\\=>y=12-9=3$

∴ Original number = 93