| If \[x+\frac{1}{y}=1\] and \[y+\frac{1}{z}=1,\] then find the value of \[z+\frac{1}{x}.\] |
A) 0
B) 1
C) 2
D) 4
Correct Answer: B
Solution :
| \[x+\frac{1}{y}=1\] (i) |
| \[y+\frac{1}{z}=1\] ... (ii) |
| \[\Rightarrow \] \[x=1-\frac{1}{y}=\frac{y-1}{y}\]\[\Rightarrow \]\[\frac{1}{x}=\frac{y}{y-1}\] |
| Again, \[y+\frac{1}{z}=1\] |
| \[\Rightarrow \] \[\frac{1}{z}=1-y\]\[\Rightarrow \]\[z=\frac{1}{1-y}\] |
| By putting the value, |
| \[z+\frac{1}{x}=\frac{1}{1-y}+\frac{y}{y-1}=\frac{y-1}{y-1}=1\] |
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