The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9 less than three times the original number. What is the original number? Thank you!

Question

18325 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-09T16:42:39

Number is $27$ .

Let the unit digit be $x$ and tens digit be $y$

then $x+y=9$ ........................(1)

and number is $x+10y$

On reversing the digits it will become $10x+y$

As $10x+y$ is $9$ less than three times $x+10y$ , we have

$10x+y=3(x+10y)-9$

or $10x+y=3x+30y-9$

or $7x-29y=-9$ ........................(2)

Multiplying (1) by $29$ and adding to (2), we get

$36x=9xx29-9=9xx28$

or $x=(9xx28)/36=7$

and hence $y=9-7=2$

and number is $27$ .