ABC26GN0983 · Simplification
Subject: General Aptitude · Chapter: Simplification · Exam: · Marks: · Difficulty:
If $\frac{a}{x}+\frac{y}{b}=1$ and $\frac{b}{y}+\frac{z}{c}=1$, then $\frac{x}{a}+\frac{c}{z}$ will be equal to:
(a)0
(b)$\frac{b}{y}$
(c)1
(d)$\frac{y}{b}$
Answer
Explanation
$\frac{a}{x}+\frac{y}{b}=1 \Rightarrow \frac{a}{x}=1-\frac{y}{b}=\frac{b-y}{b} \Rightarrow \frac{x}{a}=\frac{b}{b-y}$. $$\begin{aligned} & \frac{b}{y}+\frac{z}{c}=1 \Rightarrow \frac{z}{c}=1-\frac{b}{y}=\frac{y-b}{y} \Rightarrow \frac{c}{z}=\frac{y}{y-b}=\frac{-y}{(b-y)} . \\ & \therefore \quad \frac{x}{a}+\frac{c}{z}=\frac{b}{(b-y)}-\frac{y}{(b-y)}=\frac{(b-y)}{(b-y)}=1 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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