Answer
The number is $25$
Work Step by Step
Let the unit place digit is '$x$' and tens place digit is '$y$'. As the sum of digits is $7$, therefore-
$x+y$ = $7$ __eq.1
Now, original number = $ 10y+x$
And number formed by reversing the digits = $10x+y$
According to problem-
$(10x+y)$ - $ (10y+x)$ = $27$
i.e. $10x+y - 10y-x$ = $27$
i.e. $9x - 9y$ = $27$
Dividing by $9$ on both the sides-
i.e. $x - y$ = $3$ __eq.2
Substituting for '$x$' in eq.2 from eq.1-
$(7-y) - y$ = $3$
i.e. $7- 2y$ = $3$
i.e. $2y$ = $7-3$ = $4$
i.e. $y$ = $2$
from eq.1-
$x$= $7-y$ = $7-2$ = $5$
Therefore number is $25$
