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: $ab$
Answer (1)
12th Jan, 2024
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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