Question : If $x(x+y+z)=20$, $y(x+y+z)=30$, and $z(x+y+z)=50$, then the value of $2(x+y+z)$ is:
Option 1: 20
Option 2: –10
Option 3: 15
Option 4: 18
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Correct Answer: 20
Solution :
Given: $x(x+y+z)=20$, $y(x+y+z)=30$, and $z(x+y+z)=50$
Adding all the equations,
⇒ $x(x+y+z) + y(x+y+z) + z(x+y+z) = 20+30+50$
⇒ $(x+y+z)^{2} = 100$
⇒ $(x+y+z) = 10$
Thus, $2(x+y+z) = 20$
Hence, the correct answer is 20.
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