Three boys share some oranges .the first one gets 1/3of the total,the second one gets 2/3 if the remainder if the last boy has 12of the remains oranges how many were shared

Let $T$ be the total number of oranges.
The first boy gets $\frac{1}{3}$ of the total oranges.
Oranges for the first boy $= \frac{1}{3} T$.

Remaining oranges after the first boy $= T - \frac{1}{3} T = \frac{3}{3} T - \frac{1}{3} T = \frac{2}{3} T$.

The second boy gets $\frac{2}{3}$ of the remainder from Step 2.
Oranges for the second boy $= \frac{2}{3} \times \left(\frac{2}{3} T\right) = \frac{4}{9} T$.

Remaining oranges after the second boy $= \frac{2}{3} T - \frac{4}{9} T$.
To subtract these fractions, find a common denominator, which is 9.
$\frac{2}{3} T = \frac{2 \times 3}{3 \times 3} T = \frac{6}{9} T$.
So, remaining oranges $= \frac{6}{9} T - \frac{4}{9} T = \frac{2}{9} T$.

The last boy has 12 oranges, which is the final remainder calculated in Step 4.

To solve for $T$, multiply both sides by $\frac{9}{2}$:

The total number of oranges shared was 54.

The total number of oranges shared was $\text{54}$.