Answer
$483$
Work Step by Step
Let the ones-place digit is $z$,
the tens-place digit is $y$, and
the hundreds-place digit is $x$
Three digit number is $xyz$
Sum of the digits is $15$
$x+y+z=15$ Equation $(1)$
Tens-place digit is twice the hundreds-place digit
$y=2x$
Ones-place digit is one less than the hundreds-place digit
$z=x-1$
Substituting $y=2x$ and $z=x-1$ in Equation $(1)$
$x+y+z=15$
$x+2x+x-1=15$
$4x-1=15$
$4x=16$
$x=4$
$y=2x$
$y=2(4) = 8$
$z=x-1$
$z=4-1$
$z=3$
Three digit number is $xyz = 483$
