What is the fraction of current taken by this resistor?
Since I3 is the current flowing through the loop of the supply and the output resistor is common to loop 1 and 2, I1 - I2 will be the current flowing through it, i.e., the output current. So, I guess the answer will be the ratio of I3 and I1 - I2.

Edit







simulate this circuit &ndash; Schematic created using CircuitLab

Let the current in Loops 1, 2, 3 be I1, I2, I3 resp. The answer is independent of the source voltage, so assuming a value will make the solving part easier and won't change the answer. The Mesh matrix is,
\begin{bmatrix}
380 &amp; -120 &amp; -80\\
-120 &amp; 380 &amp; -180\\
-80 &amp; -180 &amp; 260
\end{bmatrix}
If the source voltage was 10V, the I1 = 0.0333, I2 = 0.05, I3 = 0.0833. So I3 / I2 - I1 = 4.989 which can be approximated to 5.
PS: You can try without assuming a value for source voltage