Question : If $\frac{a}{1-2a}+\frac{b}{1-2b}+\frac{c}{1-2c}=\frac{1}{2}$, then the value of $\frac{1}{1-2a}+\frac{1}{1-2b}+\frac{1}{1-2c}$ is:
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
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Correct Answer: 4
Solution :
Given: $\frac{a}{1-2a}+\frac{b}{1-2b}+\frac{c}{1-2c}=\frac{1}{2}$
Multiplying by 2 on both sides
⇒ $\frac{2a}{1-2a}+\frac{2b}{1-2b}+\frac{2c}{1-2c}=1$
Adding 3 on both sides
⇒ $1+\frac{2a}{1-2a}+1+\frac{2b}{1-2b}+1+\frac{2c}{1-2c}=1+3$
⇒ $\frac{1}{1-2a}+\frac{1}{1-2b}+\frac{1}{1-2c}=4$
Hence, the correct answer is 4.
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