Question

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

54 less than the original number. Find the original number.​

Answer 1

93

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=(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=(18)/(2) =9`

Putting the value of x in eqn(1),

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

∴ Original number = 93