<s>[INST] $\text{If } x(x+y+z)=20,y(x+y+z)=30 \text{ and } z(x+y+z)=50 \text{ then the value of } 2(x+y+z) is:$ 
If $x(x+y+z)=20$, $y(x+y+z)=30$ and $z(x+y+z)=50$ then what is the value of $2(x+y+z)$?

Ans. $20$
I have tried the following:
$$ \frac{20}{x}=\frac{30}{y}=\frac{50}{z}$$
From which I get:
$$x:y:z=2:3:5$$
Now,
$$2(x+y+z)=\frac{20}{x}+\frac{30}{y}$$
$$\implies\frac{20y+30x}{xy}$$
$$\implies\frac{20*\frac{3z}{5}+30*\frac{2z}{5}}{\frac{2z}{5}\frac{3z}{5}}$$
Which gives me
$$\frac{100}{z}$$
Back to the 3rd equation!
 [/INST] $$x(x+y+z)=20,\\ y(x+y+z)=30\\ z(x+y+z)=50\\ $$ by summing all these three eqatuations$$\left( x+y+z \right) \left( z+y+x \right) =100\\ { \left( x+y+z \right)  }^{ 2 }=100\\ x+y+z=\pm 10$$
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