In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If $Q-S=2S$ and $T=R+S+3$, then what is the value of $P+R-T$?

The correct option is 2.

Let's break down the solution step-by-step to find the value of $P+R-T$.

We are given that the letters $P$, $Q$, $R$, $S$, and $T$ represent the numbers 4, 5, 10, 12, and 15 in some order.

We are given two equations:
1) $Q-S=2S$
2) $T=R+S+3$

First, let's simplify the first equation:
Add $S$ to both sides:
$Q=3S$

Now, let's look at our set of available numbers: {4, 5, 10, 12, 15}.
We need to find two numbers from this set such that one is exactly three times the other (since $Q=3S$).
Looking at the set, the only pair that satisfies this relationship is 5 and 15, because:
$15=3\times 5$
Therefore, we must have:
$S=5$
$Q=15$

Now, the remaining numbers for $P$, $R$, and $T$ are {4, 10, 12}.

Next, let's substitute $S=5$ into the second equation:
$T=R+5+3$
Which simplifies to:
$T=R+8$

We need to choose $T$ and $R$ from the remaining set {4, 10, 12} such that $T$ is 8 more than $R$.
Checking the numbers:
If $R=4$, then $T=4+8=12$. Both 4 and 12 are in our remaining set.
Therefore, we must have:
$R=4$
$T=12$

Now, the only remaining number in the set {4, 10, 12} is 10.
Since $P$ is the only letter left, we have:
$P=10$

To summarize, the values assigned to each letter are:
$P=10$
$Q=15$
$R=4$
$S=5$
$T=12$

Finally, we calculate the required value of $P+R-T$:
$P+R-T=10+4-12$
$10+4-12=14-12=2$

Thus, the value of $P+R-T$ is indeed 2.