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The above is the requirement, I have configured a circuit as shown below


simulate this circuit – Schematic created using CircuitLab

I have solved the above schematic using superposition and deduced that \$R_1:R_3 = 3:1\$, but I could not get the required output.

Superposition node voltages:

When \$V_1 = 0\$, $$V_{\text{node}} = \frac{R_2V_1}{R_1+R_2+R_1R_2}$$

When \$V_2 = 0\$, $$V_{\text{node}} = \frac{R_1V_2}{R_1+R_2+R_1R_2}$$

I have mapped the coefficients and deduced the above ratio.


Using superposition you can show that:

(R1||R2||R3)/R1 = 1/2


(R1||R2||R3)/R2 = 1/6

So if we set R1||R2||R3 = 10K (a more-or-less arbitrary choice)

R1 = 20K

R2 = 60K

R3 = 1/(1/10K - 1/20K - 1/60K) = 30K

Let's simulate it:

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