Step 1: Express digits in terms of a variable $k$

Given that the units', tens', and hundreds' digits are in the ratio $1: 2: 3$, we can let the digits be: Units $= k$, Tens $= 2k$, Hundreds $= 3k$.

$\text{Digits} = (3k, 2k, k)$

Step 2: Formulate the number and its reverse

The 3-digit number is $N = 100(3k) + 10(2k) + k = 321k$. The number with digits in reverse order is $N' = 100(k) + 10(2k) + 3k = 123k$.

$N = 321k, \quad N' = 123k$

Step 3: Set up the sum equation

The sum of the number and its reverse is given as $1332$. Therefore: $321k + 123k = 1332$

$444k = 1332$

Step 4: Solve for $k$ and find the number

Dividing both sides by $444$, we get $k = \frac{1332}{444} = 3$. Substituting $k = 3$, the hundreds' digit is $3(3) = 9$, the tens' digit is $2(3) = 6$, and the units' digit is $1(3) = 3$.

$k = 3 \implies \text{Number} = 963$