Question : If $\frac{11-13x}{x}+\frac{11-13y}{y}+\frac{11-13z}{z}=5$, then what is the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$?
Option 1: $1$
Option 2: $\frac{13}{11}$
Option 3: $\frac{13}{5}$
Option 4: $4$
Correct Answer: $4$
Solution :
Given:
$\frac{11-13x}{x}+\frac{11-13y}{y}+\frac{11-13z}{z}=5$
$⇒\frac{11}{x}-\frac{13x}{x}+\frac{11}{y}-\frac{13y}{y}+\frac{11}{z}-\frac{13z}{z}=5$
$⇒\frac{11}{x}+\frac{11}{x}+\frac{11}{x}-39=5$
$⇒11(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})=44$
$\therefore\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{44}{11}=4$
Hence, the correct answer is $4$.
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