Question

The sum of the digits of a two digit number is $10$. If the digits are reversed, the new number is $72$ more than the original. Find the number.

• A. $18$
• B. $19$
• C. $20$
• D. $21$

Answer 1

The correct option is B $19$

Let x and y be the two digit number
$x=$tens digit
$y=$ units digit
$x+10y=$ reversed number
Sum of the $2$-digits, $x+y=10$ ---(1)
As per the condition, we write the equation as
$x+10y=72+10x+y$
Grouping the like terms,
$10y-y=10x-x+72$
$9y=9x+72$
Both sides divide by $9$,
$y=x+8$
Substitute the $y$ value in equation (1)
$x+x+8=10$
$2x=10-8$
$2x=2$
$x=1$
Put the value of $x$ in equation (1)
$1+y=10$
$y=10-1$
$y=9$
So, the number is $19$.

So, option B is correct.