Question : If $a+\frac{1}{b}=1$, $b+\frac{1}{c}=1$ , then the value of $(abc)$ is:
Option 1: $0$
Option 2: $–1$
Option 3: $1$
Option 4: $ab$
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Correct Answer: $–1$
Solution : Given: $a+\frac{1}{b}=1$, $b+\frac{1}{c}=1$. $a+\frac{1}{b}=1$ $ab+1=b$ (equation 1) Also, $b+\frac{1}{c}=1$ $1–\frac{1}{c}=b$ (equation 2) Substitute the value of b in equation 1, we get $ab+1=1–\frac{1}{c}$ $ab=–\frac{1}{c}$ $abc=–1$ Hence, the correct answer is $–1$.
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