Question

The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.

Answer 1

Let us consider,

One's digit of a two digit number $=x$ and

Then's digit $=y$

So, the number is $x+10y$

By interchanging the digits,

One's digit $=y$ and

Ten's digit $=x$

Number is $y+10x$

As per the statement,

$x+y=12$.....(1)

$y+10x=x+10y+18$

$y+10x-x-10y=18$

$x-y=2$....(2)

Adding (1) and (2), we have

$2x=14$ or $x=7$

On subtracting (1) from (2),

$2y=10$ or $y=5$

Answer:

number $=7+10\times 5=57$