ABC26GN0978 · Simplification
Subject: General Aptitude · Chapter: Simplification · Exam: 2005 · Marks: · Difficulty:
If $\frac{x}{(2 x+y+z)}=\frac{y}{(x+2 y+z)}=\frac{z}{(x+y+2 z)}=a$, then find $a$ if $x+y+z \neq 0$.
(a)$\frac{1}{3}$
(b)$\frac{1}{4}$
(c)$\frac{1}{2}$
(d)$\frac{1}{8}$
Answer
Explanation
$$\begin{aligned} & \frac{x}{(2 x+y+z)}=a \Rightarrow x=a(2 x+y+z) \\ & \frac{y}{(x+2 y+z)}=a \Rightarrow y=a(x+2 y+z) \\ & \frac{z}{(x+y+2 z)}=a \Rightarrow z=a(x+y+2 z) \end{aligned}$$ Adding (i), (ii) and (iii), we get: $x+y+z$ $$=a(4 x+4 y+4 z) \Rightarrow a=\frac{x+y+z}{4(x+y+z)}=\frac{1}{4} .$$
Explanation as extracted from the printed page; notation may be imperfect.
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