Question

The sum of the digits of a 2-digit number is $7$ if the digits are reversed the number obtained exceeds the original numbers by $27$. Find the number.

Answer 1

Let the 2-digit number lie $10x+y$ x,y > 0

$x+y=7$ ________(1)

When digits are reversed, the number becomes $\Rightarrow 10y+x$

$10y+x=10x+y+27$

$9y-9x=27$

$y-x=3$ _______(2)

$\left(1\right)+\left(2\right)$

$2y=10$

$y=5$

$x+5=7$

$x=2$

Number = $10\left(2\right)+5$

$=20+5$

$=25$